2.1: Tap-Out
Serves: 10—15 Players
Cook Time: 10 min
Ingredients
- 10—15 Players
- An Audience ‘Ask For’
- Example object ‘Ask For’
- Trash can
- Fire Truck
- Cell Phone
- Toilet
Instructions
- One player makes an ‘ask’ for an object, item, or scenario
- At any time players may call ‘freeze’ and enter the scene
- Every time a player enters the scene, the scene must change completely, but be connected to whatever action or position was taking place in the previous scene.
- Only two players may be active at any time.
Notes
In ‘Tap Out’ all players arrange themselves in a ring or line, with one player to begin the game. This player makes an ‘ask for’: object, item, situation, etc. and begins the scene. At any time one player may call ‘freeze’ and enter the scene. Once a player has entered the scene they must change it completely, but have some connection to the position or actions taking place in the previous scene. The game works the best when done quickly, typically no more than 15-30 seconds should lapse before someone changes the scene. Linking the scenes to current events or humorous stories in the news also greatly increases the effectiveness of the game.


17: Electrochemistry
Electrochemistry deals with chemical reactions that produce electricity and the changes associated with the passage of electrical current through matter. The reactions involve electron transfer, and so they are oxidation-reduction (or redox) reactions. Many metals may be purified or electroplated using electrochemical methods. Devices such as automobiles, smartphones, electronic tablets, watches, pacemakers, and many others use batteries for power. Batteries use chemical reactions that produce electricity spontaneously and that can be converted into useful work. All electrochemical systems involve the transfer of electrons in a reacting system. In many systems, the reactions occur in a region known as the cell, where the transfer of electrons occurs at electrodes.
-
- 17.1: Review of Redox Chemistry
- An electric current consists of moving charge. The charge may be in the form of electrons or ions. Current flows through an unbroken or closed circular path called a circuit. The current flows through a conducting medium as a result of a difference in electrical potential between two points in a circuit. Electrical potential has the units of energy per charge. In SI units, charge is measured in coulombs (C), current in amperes, and electrical potential in volts.
-
- 17.2: Galvanic Cells
- Electrochemical cells typically consist of two half-cells. The half-cells separate the oxidation half-reaction from the reduction half-reaction and make it possible for current to flow through an external wire. One half-cell contains the anode. Oxidation occurs at the anode. The anode is connected to the cathode in the other half-cell. Reduction occurs at the cathode. Adding a salt bridge completes the circuit allowing current to flow.
-
- 17.3: Electrode and Cell Potentials
- Assigning the potential of the standard hydrogen electrode (SHE) as zero volts allows the determination of standard reduction potentials, E°, for half-reactions in electrochemical cells. As the name implies, standard reduction potentials use standard states (1 bar or 1 atm for gases; 1 M for solutes, often at 298.15 K) and are written as reductions (where electrons appear on the left side of the equation).
-
- 17.4: Potential, Free Energy, and Equilibrium
- Electrical work is the negative of the product of the total charge (Q) and the cell potential (Ecell). The total charge can be calculated as the number of moles of electrons (n) times the Faraday constant (F = 96,485 C/mol e−). Electrical work is the maximum work that the system can produce and so is equal to the change in free energy. Thus, anything that can be done with or to a free energy change can also be done to or with a cell potential.
-
- 17.5: Batteries and Fuel Cells
- Batteries are galvanic cells, or a series of cells, that produce an electric current. When cells are combined into batteries, the potential of the battery is an integer multiple of the potential of a single cell. There are two basic types of batteries: primary and secondary. Primary batteries are “single use” and cannot be recharged. Dry cells and (most) alkaline batteries are examples of primary batteries. The second type is rechargeable and is called a secondary battery.
-
- 17.6: Corrosion
- Corrosion is the degradation of a metal caused by an electrochemical process. Large sums of money are spent each year repairing the effects of, or preventing, corrosion. Some metals, such as aluminum and copper, produce a protective layer when they corrode in air. The thin layer that forms on the surface of the metal prevents oxygen from coming into contact with more of the metal atoms and thus “protects” the remaining metal from further corrosion. Iron corrodes (forms rust) when exposed to wate
-
- 17.7: Electrolysis
- Using electricity to force a nonspontaneous process to occur is electrolysis. Electrolytic cells are electrochemical cells with negative cell potentials (meaning a positive Gibbs free energy), and so are nonspontaneous. Electrolysis can occur in electrolytic cells by introducing a power supply, which supplies the energy to force the electrons to flow in the nonspontaneous direction. Electrolysis is done in solutions, which contain enough ions so current can flow.
-
- 17.11: Exercises
- These are homework exercises to accompany the Textmap created for "Chemistry" by OpenStax. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.


Apply the rules of medical language to build, analyze, spell, pronounce, abbreviate, and define terms as they relate to the blood
Identify meanings of key word components of the blood
Spell medical terms of the blood vessels and blood and use correct abbreviations
Categorize diagnostic, therapeutic, procedural or anatomic terms related to the blood
Use terms related to the blood
Use terms related to the diseases and disorders of the blood
Blood Vessels and Blood Word Parts
Click on prefixes, combining forms, and suffixes to reveal a list of word parts to memorize for the Cardiovascular System – Blood.
Query \(\PageIndex{1}\)
Introduction to the Blood Vessels and Blood
Our large, complex bodies need blood to deliver nutrients to and remove wastes from our trillions of cells. The heart, as discussed in the previous chapter, pumps blood throughout the body in a network of blood vessels. Together, these three components—blood, heart, and vessels—makes up the cardiovascular system.
Virtually every cell, tissue, organ, and system in the body is impacted by the circulatory system. This includes the generalized and more specialized functions of transport of materials, capillary exchange, maintaining health by transporting white blood cells and various immunoglobulins (antibodies), hemostasis, regulation of body temperature, and helping to maintain
acid-base
balance. Table 10.1 summarizes the important relationships between the circulatory system and the other body systems.
Table 10.1 Interaction of the Circulatory System with Other Body Systems. A table depicting the various body systems and the role of the circulatory system in each. Adapted from Betts, et al., 2021. Licensed under
CC BY 4.0
.
SYSTEM
ROLE OF CIRCULATORY SYSTEM
Digestive
Absorbs nutrients and water; delivers nutrients (except most lipids) to liver for processing by hepatic portal vein; provides nutrients essential for hematopoiesis and building hemoglobin.
Endocrine
Delivers hormones: atrial natriuretic hormone (peptide) secreted by the heart atrial cells to help regulate blood volumes and pressures; epinephrine, ANH, angiotensin II, ADH, and thyroxine to help regulate blood pressure; estrogen to promote vascular health in women and men.
Integumentary
Carries clotting factors, platelets, and white blood cells for hemostasis, fighting infection, and repairing damage; regulates temperature by controlling blood flow to the surface, where heat can be dissipated; provides some coloration of integument; acts as a blood reservoir.
Lymphatic
Transports various white blood cells, including those produced by lymphatic tissue, and immunoglobulins (antibodies) throughout the body to maintain health; carries excess tissue fluid not able to be reabsorbed by the vascular capillaries back to the lymphatic system for processing.
Muscular
Provides nutrients and oxygen for contraction; removes lactic acid and distributes heat generated by contraction; muscular pumps aid in venous return; exercise contributes to cardiovascular health and helps to prevent atherosclerosis.
Nervous
Produces cerebrospinal fluid (CSF) within choroid plexuses; contributes to blood-brain barrier; cardiac and vasomotor centers regulate cardiac output and blood flow through vessels via the autonomic system.
Reproductive
Aids in erection of genitalia in both sexes during sexual arousal; transports gonadotropic hormones that regulate reproductive functions.
Respiratory
Provides blood for critical exchange of gases to carry oxygen needed for metabolic reactions and carbon dioxide generated as byproducts of these processes.
Skeletal
Provides calcium, phosphate, and other minerals critical for bone matrix; transports hormones regulating buildup and absorption of matrix including growth hormone (somatotropin), thyroid hormone, calcitronins, and parathyroid hormones; erythropoietin stimulates myeloid cell hematopoiesis; some level of protection for select vessels by bony structures.
Urinary
Delivers 20% of resting circulation to kidneys for filtering, reabsorption of useful products, and secretion of excesses; regulates blood volume and pressure by regulating fluid loss in the form of urine and by releasing the enzyme renin that is essential in the renin-angiotensin-aldosterone mechanism.
Cardiovascular System – Blood Vessels and Blood Medical Terms
Query \(\PageIndex{2}\)
Anatomy of the Blood Vessels
Blood pumped by the heart flows through a series of vessels known as arteries, arterioles, capillaries, venules, and veins before returning to the heart.
Arteries
transport blood away from the heart and branch into smaller vessels, forming arterioles.
Arterioles
distribute blood to capillary beds, the sites of exchange with the body tissues.
A
capillary
is a microscopic channel that supplies blood to the tissues themselves, a process called
perfusion.
Exchange of gases and other substances occurs in the capillaries between the blood and the surrounding cells and their tissue fluid (interstitial fluid).
For capillaries to function, their walls must be leaky, allowing substances to pass through.
Capillaries
lead back to small vessels known as
venules.
Venules
are small veins that converge into larger veins.
A
vein
is a blood vessel that conducts blood toward the heart
Compared to arteries, veins are thin-walled vessels with large and irregular lumens
Larger veins are commonly equipped with valves that promote the unidirectional flow of blood toward the heart and prevent backflow toward the capillaries caused by the inherent low blood pressure in veins as well as the pull of gravity
Other ways in which the body assists the transport of venous blood back to the heart involve contractions of skeletal muscles in the extremities (see figure below
), as well as pressure variations caused by breathing motion in the chest.
Concept Check
Select the correct bolded word: A
rteries always carry blood
away from/towards
the heart
Select the correct bolded word: Veins always carry blood
away from/towards
the heart.
Both arteries and veins have the same three distinct tissue layers, called
tunics
, for the garments first worn by ancient Romans. From the most interior layer to the outer, these tunics are the
tunica intima,
the
tunica media
, and the
tunica externa
. The smooth muscle in the middle layer, the tunica media, provides the vessel with the ability to vasoconstrict and vasodilate as needed to ensure sufficient blood flow. The table below compares the features of arteries and veins.
Table 10.2.
Comparison of Arteries and Veins. From Betts, et al., 2021. Licensed under CC BY 4.0.
CHARACTERISTIC
ARTERIES
VEINS
Direction of blood flow
Conducts blood away from the heart
Conducts blood toward the heart
General appearance
Rounded
Irregular, often collapsed
Pressure
High
Low
Wall thickness
Thick
Thin
Relative oxygen concentration
Higher in systemic arteries
Lower in pulmonary arteries
Lower in systemic veins
Higher in pulmonary veins
Valves
Not present
Present most commonly in limbs and in veins inferior to the heart
The Major Arteries and Veins in the Human Body
Many arteries and veins share the same names, parallel one another throughout the body, and are very similar on the right and left sides of the body. For example, you will find a pair of
femoral
arteries and a pair of femoral veins, with one vessel on each side of the body. In contrast, some vessels closer to the midline of the body, such as the aorta, are unique and not paired.
Names of vessels may change with location. Like a street that changes name as it passes through an intersection, an artery or vein can change names as it passes an anatomical landmark. For example, the left
subclavian
artery becomes the
axillary
artery as it passes into the axillary region, and then becomes the
brachial
artery as it enters the upper arm.
The next two diagrams illustrate the major arteries and veins in the human body.
Figure 10.1 Systemic Arteries. The major systemic arteries shown here deliver oxygenated blood throughout the body. From Betts, et al., 2021. Licensed under
CC BY 4.0
.
Figure 10.2 Major Systemic Veins of the Body. The major systemic veins of the body are shown here in an anterior view. From Betts, et al., 2021. Licensed under
CC BY 4.0
.
Concept Check
Without looking back at the images of the main arteries and veins of the body, can you
name
and
locate
3 arteries and 3 veins in your body?
Physiology of the Blood Vessels
Arteries and veins transport blood in two distinct circuits: the
systemic circuit
and the
pulmonary circuit
. Systemic arteries provide blood rich in oxygen to the body’s tissues. The blood returned to the heart through systemic veins has less oxygen, since much of the oxygen carried by the arteries has been delivered to the cells. In contrast, in the pulmonary circuit, arteries carry blood low in oxygen exclusively to the lungs for gas exchange. Pulmonary veins then return freshly oxygenated blood from the lungs to the heart to be pumped back out into systemic circulation.
Figure 10.3 Cardiovascular Circulation. The pulmonary circuit moves blood from the right side of the heart to the lungs and back to the heart. The systemic circuit moves blood from the left side of the heart to the head and body and returns it to the right side of the heart to repeat the cycle. The arrows indicate the direction of blood flow, and the colors show the relative levels of oxygen concentration. From Betts, et al., 2021. Licensed under
CC BY 4.0
.
Blood Pressure
Blood pressure
is
the force exerted by blood upon the walls of the blood vessels or the chambers of the heart. Blood pressure may be measured in capillaries and veins, as well as the vessels of the pulmonary circulation; however, the general term ‘blood pressure’ refers to the pressure of blood flowing in the arteries of the systemic circulation.
Blood pressure is one of the critical parameters measured on virtually every patient in every healthcare setting.
The technique used today was developed more than 100 years ago by a pioneering Russian physician, Dr. Nikolai Korotkoff. Turbulent blood flow through the vessels can be heard as a soft ticking while measuring blood pressure; these sounds are known as
Korotkoff sounds
. B
lood pressure is measured in mm Hg and is usually obtained from the brachial artery
using a sphygmomanometer and a stethoscope. Blood pressure is recorded as
systolic pressure
over
diastolic pressure.
Did You Know?
120/80
mm Hg is a normal, healthy blood pressure.
60-100
beats per minute is a normal, resting, adult pulse.
Five variables influence blood flow and blood pressure:
Cardiac output
Vessel Compliance
Volume of the blood
Viscosity of the blood
Blood vessel length and diameter
Pulse
Each time the heart ejects blood forcefully into the circulation, the arteries must expand and then
recoil
to
accommodate
the surge of blood moving through them. This expansion and recoiling of the arterial wall is called the
pulse
and allows us to measure heart rate. Pulse can be palpated manually by placing the tips of the fingers across an artery that runs close to the body surface, such as the radial artery or the common carotid artery. These sites and other pulse sites are shown in the figure below.
Both the rate and the strength of the pulse are important clinically. A high or irregular pulse rate can be caused by physical activity or other temporary factors, but it may also indicate a heart condition. The pulse strength indicates the strength of ventricular contraction and cardiac output. If the pulse is strong, then systolic pressure is high. If it is weak, systolic pressure has fallen, and medical intervention may be warranted.
Figure 10.4 Pulse Sites. The pulse is most readily measured at the radial artery, but can be measured at any of the pulse points shown. From Betts, et al., 2021. Licensed under
CC BY 4.0
.
The Composition (Anatomy) of Blood and the Functions of the Components
Blood
is a connective tissue made up of cellular elements and an extracellular matrix. The cellular elements are referred to as the
formed elements and
include
red blood cells (RBCs)
,
white blood cells (WBCs)
, and
platelets
. The extracellular matrix, called
plasma
, makes blood unique among connective tissues because it is fluid. This fluid, which is mostly water, perpetually suspends the formed elements and enables them to circulate throughout the body within the cardiovascular system.
Did You Know?
Blood constitutes approximately 8% of adult body weight.
In the laboratory, blood samples are often centrifuged in order to separate the components of blood from one another (see the figure below). Erythrocytes are the heaviest elements in blood and settle at the very bottom of the tube. Above the erythrocyte layer we see the
buffy coat
, a pale, thin layer of leukocytes and thrombocytes, which together make up less than 1% of the sample of whole blood. Above the buffy coat is the blood plasma, normally a pale, straw-colored fluid, which constitutes the remainder of the sample.
In normal blood, about 45 percent of a sample is erythrocytes, which is referred to as the hematocrit. The hematocrit of any one sample can vary significantly, however, about 36–50 percent, according to gender and other factors. Not counting the buffy coat, which makes up less than 1% of the blood, we can estimate the mean plasma percentage to be the percent of blood that is not erythrocytes: approximately 55%.
Figure 10.5 Composition of Blood: Two tubes of EDTA-anticoagulated blood. Left tube: after standing, the RBCs have settled at the bottom of the tube. Reused from Libretext Anatomy & Physiology
Blood Plasma
Like other fluids in the body, plasma is composed primarily of water. In fact, it is about 92% water. Dissolved or suspended within this water is a mixture of substances, most of which are proteins.
The major components of plasma and their functions are summarized in the table below.
Formed Elements (Erythrocytes, Leukocytes, Thrombocytes)
The table below summarizes the main facts about the formed elements in blood.
Table 10.3 Summary of Formed Elements in Blood. Adapted from Betts, et al., 2021. Licensed under
CC BY 4.0.
FORMED ELEMENT
MAJOR SUBTYPES
NUMBER PRESENT PER MICROLITER (
µL)
AND MEAN (RANGE)
APPEARANCE IN A STANDARD BLOOD SMEAR
SUMMARY OF FUNCTIONS
COMMENTS
Erythrocytes (red blood cells)
Red Blood Cell
n/a
5.2 million ( 4.4-5.0 million)
Flattened biconcave disk; no nucleus; pale red colour
Transport oxygen and some carbon dioxide between tissues and lungs
Lifespan of approximately 120 days
Leukocytes (white blood cells)
n/a
7000 (5000 – 10,000)
Obvious dark-staining nucleus
All function in body defenses
Exit capillaries and move into tissues; lifespan of usually a few hours or days
Leukocytes (white blood cells) Types
Granulocytes including neutrophils, eosinophils, and basophils
4360 (1800-9950)
Abundant granules in cytoplasm; nucleus normal lobed
Nonspecific (innate) resistance to disease
Classified according to membrane-bound granules in cytoplasm
Neutrophils
Neutrophil Cell
4150 (1800-7300)
Nuclear lobes increase with age; pale lilac granules
Phagocytic; particularly effective against bacteria. Release cytotoxic chemicals from granules
Most common leukocyte; lifespan of minutes to days
Eosinophils
Eosinophils Cell
165 (0-700)
Nucleus generally two-lobed; bright red-orange granules
Phagocytic cells; particularly effective with antigen-antibody complexes. Release antihistamines. Increase in allergies and parasitic infections
Lifespan of minutes to days
Basophils
Basophil Cell
44 (0-150)
Nucleus generally two-lobed but difficult to see due to presence of heavy, dense, dark purple granules
Promotes inflammation
Least common leukocyte; lifespan unknown
Agranulocytes including lymphocytes and monocytes
2640 (1700-4950)
Lack abundant granules in cytoplasm; have a simple-shaped nucleus that may be indented
Body defenses
Group consists of two major cell types from different lineages
Lymphocytes
Lymphocytes Cell
2185 (1500-4000)
Spherical cells with a single often large nucleus occupying much of the cell’s volume; stains purple; see in large (natural killer cells) and small (B and T cells) variants
Primarily specific (adaptive) immunity; T cells directly attack other cells (cellular immunity). B cells release antibodies (humoral immunity); natural killer cells are similar to T cells but nonspecific
Initial cells originate in bone marrow, but secondary production occurs in lymphatic tissue; several distinct subtypes; memory cells form after exposure to a pathogen and rapidly increase responses to subsequent exposure; lifespan of many years
Monocytes
Monocytes Cell
455 (200-950)
Largest leukocyte with an indented or horseshoe-shaped nucleus
Very effective phagocytic cells engulfing pathogens or worn out cells; also serve as antigen-presenting cells (APCs) for other components of the immune system
Produced in red bone marrow; referred to as macrophages after leaving circulation
Platelets
Platelete Cells
n/a
350,000 (150,000 – 500,000)
Cellular fragments surrounded by a plasma membrane and containing granules; purple stain
Hemostasis plus release growth factors for repair and healing of tissue
Formed from megakaryocytes that remain in the red bone marrow and shed platelets into circulation
Erythrocytes
The most abundant formed elements in blood, erythrocytes are basically sacs packed with an oxygen-carrying compound called hemoglobin. Production of erythrocytes in the red bone marrow occurs at the staggering rate of more than 2 million cells per second. For this production to occur, raw materials including iron, copper, zinc B-vitamins, glucose, lipids, and amino acids must be present in adequate amounts. Erythrocytes live only 120 days on average, and thus must be continually replaced. Worn-out erythrocytes are phagocytized by macrophages and their hemoglobin is broken down. The breakdown products are recycled or removed as wastes.
Figure 10.6 Shape of Red Blood Cells. Erythrocytes are biconcave discs with very shallow centers. This shape optimizes the ratio of surface area to volume, facilitating gas exchange. It also enables them to fold up as they move through narrow blood vessels. From Betts, et al., 2021. Licensed under
CC BY 4.0.
Lymphocytes are one of the types of leukocytes and will be discussed in more detail here, since they tie into the next chapter which discusses the body’s defenses The three major groups of lymphocytes include natural killer cells, B cells, and T cells.
Natural killer (NK) cells
are capable of recognizing cells that do not express “self” proteins on their plasma membrane or that contain foreign or abnormal markers. These “nonself” cells include cancer cells, cells infected with a virus, and other cells with atypical surface proteins.
B lymphocytes (B cells)
and
T lymphocytes (T cells)
, play prominent roles in defending the body against specific pathogens (disease-causing microorganisms) and are involved in specific immunity. B cells undergo a maturation process in the bone marrow, whereas T cells undergo maturation in the
t
hymus. This site of the maturation process gives rise to the name B and T cells.
Plasma cells
, a type of B cell, produce the antibodies or immunoglobulins that bind to specific foreign or abnormal components of plasma membranes.
T cells
provide immunity by physically attacking foreign or diseased cells.
Memory cells
are a variety of both B and T cells that form after exposure to a pathogen and mount rapid responses upon subsequent exposures. Unlike other leukocytes, memory cells live for many years.
Platelets
After entering the circulation, approximately one-third of the newly-formed platelets migrate to the spleen for storage for later release in response to any rupture in a blood vessel.  Platelets remain only about 10 days, then are phagocytized by macrophages.
Platelets are key players in
hemostasis
, the process by which the body seals a ruptured blood vessel and prevents further loss of blood. Although rupture of larger vessels usually requires medical intervention, hemostasis is quite effective in dealing with small, simple wounds. There are three steps to the process: vascular spasm or vasoconstriction, the formation of a platelet plug, and coagulation (blood clotting). Failure of any of these steps will result in
hemorrhage.
The figure below summarizes the steps of hemostasis.
Figure 10.8 Hemostasis. (a) An injury to a blood vessel initiates the process of hemostasis. Blood clotting involves three steps. First, vascular spasm constricts the flow of blood. Next, a platelet plug forms to temporarily seal small openings in the vessel. Coagulation then enables the repair of the vessel wall once the leakage of blood has stopped. (b) The synthesis of fibrin in blood clots lead to a common pathway. (credit a: Kevin MacKenzie). From Betts, et al., 2021. Licensed under CC BY 4.0.
Fibrinolysis is the process in which a clot is degraded in a healing vessel. An
anticoagulant
is any substance that opposes coagulation. Several circulating plasma anticoagulants play a role in limiting the coagulation process to the region of injury and restoring a normal, clot-free condition of blood.
Concept Check
Can you explain what happens in each step of
hemostasis
?
Describe an
anticoagulant
.
Physiology of Blood
Although carrying oxygen and nutrients to cells and removing wastes from cells is the main function of blood, it is important to realize that blood also serves in defense, distribution of heat, and maintenance of homeostasis.
Transportation
Nutrients from the foods you eat are absorbed in the digestive tract. Most of these travel in the bloodstream directly to the liver, where they are processed and released back into the bloodstream for delivery to body cells.
Oxygen from the air you breathe diffuses into the blood, which moves from the lungs to the heart, which then pumps it out to the rest of the body.
Endocrine glands scattered throughout the body release their products, called
hormones
, into the bloodstream, which carries them to distant target cells.
Blood also picks up
cellular wastes
and byproducts, and transports them to various organs for removal. For instance, blood moves carbon dioxide to the lungs for
exhalation
from the body, and various waste products are transported to the kidneys and liver for excretion from the body in the form of urine or bile.
Defense
Leukocytes protect the organism from disease-causing bacteria, cells with
mutated
DNA that could multiply to become cancerous, or body cells infected with viruses.
When damage to the vessels results in bleeding, blood platelets and certain proteins dissolved in the plasma, interact to block the ruptured areas of the blood vessels involved. This protects the body from further blood loss.
Homeostasis
If you were exercising on a warm day, your rising core body temperature would trigger several homeostatic mechanisms, including increased transport of blood from your core to your body periphery, which is typically cooler. As blood passes through the vessels of the skin, heat would be dissipated to the environment, and the blood returning to your body core would be cooler. In contrast, on a cold day, blood is diverted away from the skin to maintain a warmer body core. In extreme cases, this may result in frostbite.
Blood helps to regulate the water content of body cells.
Blood also helps to maintain the chemical balance of the body. Proteins and other compounds in blood act as buffers, which thereby help to regulate the pH of body tissues. The pH of blood ranges from 7.35 to 7.45.
Concept Check
These three terms all sound similar. Can you explain them by breaking down the word parts?
Hemostasis
Homeostasis
Hematopoiesis
Blood Types
In order to understand blood types, it is important to understand several terms that relate to the body’s
immune
functions (discussed in detail in the next chapter)
Antigens are substances that the body does not recognize as belonging to itself (“self”) and that therefore trigger a
defensive response
from the leukocytes of the immune system. Many people have antigens on the surfaces of their red blood cells. More than 50 antigens have been identified on erythrocyte membranes, but the most significant in terms of their potential harm to patients are classified in two groups: the ABO blood group and the Rh blood group.
Antibodies
are proteins which are produced by plasma cells in response to a “non-self” antigen being present in the body. Antibodies attach to the antigens on the plasma membranes of the erythrocytes in a blood transfusion and cause them to adhere to one another.
Agglutination
refers to the resulting clumps of red blood cells that are formed in such an antigen-antibody reaction. These clumps can block small blood vessels, thereby cutting of the supply of oxygen and nutrients to the tissues
.
Hemolysis
, or the breakdown of the erythrocyte’s cell membrane, takes place as the clumps of red cells start to degrade. The resulting release of the cell’s contents, mainly hemoglobin, into the bloodstream can cause kidney failure.
ABO Blood Group
ABO blood types are
genetically
determined. Each type is determined by the presence or absence of certain antigens on the individual’s red blood cell membrane, as well as the presence or absence of certain antibodies. Normally the body must be exposed to a
foreign antigen
before an antibody can be produced. This is not the case for the ABO blood group, in which some blood types come preloaded with their own set of antibodies against another type. The figure below shows the ABO blood group as well as the universal donor and recipient in relation to blood transfusions.
Figure 10.9 ABO Blood Groups. From Betts, et al., 2021. Licensed under
CC BY 4.0.

People who have type A blood, without any prior exposure to incompatible blood, have preformed
anti-B antibodies
circulating in their blood. These antibodies will cause a serious immune reaction if they encounter blood that has B antigens.
Blood Type B
People whose erythrocytes have
B antigens.
People with type B blood has inherent
anti-A antibodies.
Blood Type AB
People can also have
both A and B antigens
on their erythrocytes, in which case they are blood type AB.
Individuals with type AB blood,
do not have inherent antibodies
to either A or B antigens.
Blood Type O
People with
neither A nor B antigens
are designated blood type O.
People with type O blood have
both anti-A and anti-B antibodies
circulating in their blood plasma.
Rh Blood Group
The
Rh blood group
is classified according to the presence or absence of a second erythrocyte
antigen
identified as Rh.  Note that the Rh group is distinct from the ABO group, so any individual, no matter their ABO blood type, may have or lack this Rh antigen. When identifying a patient’s blood type, the Rh group is designated by adding the word positive or negative to the ABO type. For example, A positive (A+) means ABO group A blood with the Rh antigen present, and AB negative (AB−) means ABO group AB blood without the Rh antigen.
Hemolytic Disease of the Newborn (HDN)
Antibodies to the Rh antigen are produced only in Rh
−
individuals after exposure to the antigen. This process, called sensitization, occurs following a transfusion with Rh-incompatible blood or, more commonly, with the birth of an Rh
+
baby to an Rh
−
mother.
In a
first pregnancy
problems are rare
,
since the baby’s Rh
+
cells rarely cross the placenta. However, during or immediately after birth, the Rh
−
mother can be exposed to the baby’s Rh
+
cells (Figure below). Research has shown that this occurs in about 13−14 percent of such pregnancies. After exposure, the mother’s immune system begins to generate anti-Rh antibodies.
In a
second pregnancy
if a mother should conceive a Rh
+
baby, the Rh antibodies she has produced can cross the placenta into the fetal bloodstream and destroy the fetal RBCs. This condition, known as
hemolytic disease of the newborn (HDN)
or erythroblastosis fetalis. This may cause anemia in mild cases, but the agglutination and hemolysis can be so severe that without treatment the fetus may die in the womb or shortly after birth.
A drug known as RhoGAM, short for Rh immune globulin, can temporarily prevent the development of Rh antibodies in the Rh
−
mother, thereby averting this potentially serious disease for the fetus. RhoGAM antibodies destroy any fetal Rh
+
erythrocytes that may cross the placental barrier. RhoGAM is normally administered to Rh
−
mothers during weeks 26−28 of pregnancy and within 72 hours following birth.
Figure 10.10 Erythroblastosis Fetalis. The first exposure of an Rh− mother to Rh+ erythrocytes during pregnancy induces sensitization. Anti-Rh antibodies begin to circulate in the mother’s bloodstream. A second exposure occurs with a subsequent pregnancy with an Rh+ fetus in the uterus. Maternal anti-Rh antibodies may cross the placenta and enter the fetal bloodstream, causing agglutination and hemolysis of fetal erythrocytes. From Betts, et al., 2021. Licensed under
CC BY 4.0.
Blood Transfusions
Figure 10.11 is an example of a commercially produced “bedside” card which enables quick typing of both a recipient’s and donor’s blood before transfusion. The card contains three reaction sites or wells. One is coated with an anti-A antibody, one with an anti-B antibody, and one with an anti-D antibody (tests for the presence of Rh factor D). Mixing a drop of blood and saline into each well enables the blood to interact with a preparation of type-specific antibodies, also called anti-seras. Agglutination of RBCs in a given site indicates a positive identification of the blood antigens, in this case A and Rh antigens for blood type A+. To avoid serious and potentially fatal immune reactions, the donor’s and recipient’s blood types must match
Figure 10.11. Cross Matching Blood Types. From Betts, et al., 2013. Licensed under
CC BY 4.0.
To avoid transfusion reactions, it is best to transfuse only matching blood types; that is, a type B
+
recipient should ideally receive blood only from a type B
+
donor and so on. That said, in emergency situations, when acute hemorrhage threatens the patient’s life, there may not be time for cross matching to identify blood type. In these cases, blood from a
universal donor
may be transfused.
Blood Vessel Medical Terms Not Easily Broken into Word Parts
Query \(\PageIndex{3}\)
Common Diseases and Disorders of Blood Vessels and/or Blood
Arteriosclerosis
Arteriosclerosis is normally defined as the more generalized loss of compliance, “hardening of the arteries,” whereas atherosclerosis is a more specific term for the build-up of plaque in the walls of the vessel and is a specific type of arteriosclerosis.
When arteriosclerosis causes vessel compliance to be reduced, pressure and resistance within the vessel increase. This is a leading cause of hypertension and coronary heart disease, as it causes the heart to work harder to overcome this resistance. Any artery in the body can be affected by these pathological conditions, and individuals who have pathologies like coronary artery disease, may also be at risk for other vascular injuries, like strokes or peripheral arterial disease.
Atherosclerosis is a type of arteriosclerosis in which plaques form when circulating triglycerides, cholesterol and other substances seep between the damaged endothelial lining cells and become trapped within the artery wall, resulting in narrowed arteries and impaired blood flow (see Figure 10.12)
(Wikimedia Commons, 2019)
.
Figure 10.12 Atherosclerosis. This is an example of how build up of lipids (fat) in the artery prevents blood from flowing. From Blausen.com staff courtesy of Oregon State University, CC BY-SA 2.0, via Wikimedia Commons.
Sometimes a plaque can rupture, causing microscopic tears in the artery wall that allow blood to leak into the tissue on the other side. When this happens, platelets rush to the site to clot the blood. This clot can further obstruct the artery and—if it occurs in a coronary or cerebral artery—cause a sudden heart attack or stroke. Alternatively, plaque can break off and travel through the bloodstream as an embolus until it blocks a more distant, smaller artery.
Peripheral arterial disease
(PAD, also called peripheral vascular disease, PVD), occurs when atherosclerosis affects arteries in the legs. A major risk factor for both arteriosclerosis and atherosclerosis is advanced age, as the conditions tend to progress over time. There is also a distinct genetic component, and pre-existing hypertension and/or diabetes also greatly increase the risk. However, obesity, poor nutrition, lack of physical activity, and tobacco use all are major risk factors.
Treatment of atherosclerosis includes lifestyle changes, such as weight loss, smoking cessation, regular exercise, and adoption of a diet low in sodium and saturated fats. Medications to reduce cholesterol and blood pressure may be prescribed. For blocked coronary arteries, angioplasty or coronary artery bypass graft (CABG) surgery may be warranted. In an carotid endarterectomy, plaque is surgically removed from the walls of a the carotid artery, which is the main source of oxygenated blood for the brain
(Betts, et al., 2021)
.
Edema and Varicose Veins
Despite the presence of valves and the contributions of other anatomical and physiological adaptations that assist in moving blood through veins, over the course of a day, some blood will inevitably pool, especially in the lower limbs, due to the pull of gravity. Any blood that accumulates in a vein will increase the pressure within it, which can then be reflected back into the smaller veins, venules, and eventually even the capillaries. This increased pressure in the capillaries will push of fluids out of the capillaries and into the interstitial fluid, causing a condition called edema
.
Most people experience a daily accumulation of tissue fluid, especially if they spend much of their work life on their feet (like most health professionals). However, clinical edema goes beyond normal swelling and requires medical treatment. Edema has many potential causes, including hypertension and heart failure, severe protein deficiency, renal failure, and many others. In order to treat edema, which is a sign rather than a discrete disorder, the underlying cause must be diagnosed and alleviated.
Figure 10.13 Varicose Veins. Varicose veins are commonly found in the lower limbs. (credit: Nini00). From Wikimedia Commons. Licensed under CC BY-SA 3.0.
Edema may be accompanied by varicose veins, especially in the superficial veins of the legs (see Figure 10.13). This disorder arises when defective valves allow blood to accumulate within the veins, causing them to distend, twist, and become visible on the surface of the skin. Varicose veins may occur in both sexes, but are more common in women and are often related to pregnancy. More than simple cosmetic blemishes, varicose veins are often painful and sometimes itchy or throbbing. Without treatment, they tend to grow worse over time. The use of support hose, as well as elevating the feet and legs whenever possible, may be helpful in alleviating this condition
(Betts, et al., 2021)
.
Hypertension
Hypertension
is defined as chronic and persistent blood pressure measurements of 140/90 mm Hg or above. Pressures between 120/80 and 140/90 mm Hg are defined as prehypertension. Hypertension is typically a silent disorder and patients may fail to recognize the seriousness of their condition and fail to follow their treatment plan, putting them at risk for a heart attack or stroke. Hypertension may also lead to an aneurysm, peripheral arterial disease, chronic kidney disease, or heart failure
(Betts, et al., 2021)
.
Hemorrhage
Minor blood loss is managed by hemostasis and repair. Hemorrhage is a loss of blood that cannot be controlled by hemostatic mechanisms. Initially, the body responds to hemorrhage by initiating mechanisms aimed at increasing blood pressure and maintaining blood flow. Ultimately, however, blood volume will need to be restored, either through physiological processes or through medical intervention. If blood loss is less than 20 percent of total blood volume, fast-acting homeostatic mechanisms causing increased cardiac output and vasoconstriction, would usually return blood pressure to normal and redirect the remaining blood to the tissues. Blood volume will then need to be restored via slower-acting homeostatic mechanisms, to increase body fluids and erythrocyte production
(Betts, et al., 2021)
.
Circulatory Shock
The loss of too much blood may lead to
circulatory shock
, a life-threatening condition in which the circulatory system is unable to maintain blood flow to adequately supply sufficient oxygen and other nutrients to the tissues to maintain cellular metabolism. It should not be confused with emotional or psychological shock. Typically, the patient in circulatory shock will demonstrate an increased heart rate but decreased blood pressure. Urine output will fall dramatically, and the patient may appear confused or lose consciousness. Unfortunately, shock is an example of a positive-feedback loop that, if uncorrected, may lead to the death of the patient
(Betts, et al., 2021)
.
There are several recognized forms of shock:
Hypovolemic shock
in adults is typically caused by hemorrhage, although in children it may be caused by fluid losses related to severe vomiting or diarrhea.
Cardiogenic shock
results from the inability of the heart to maintain cardiac output. Most often, it results from a myocardial infarction (heart attack), but it may also be caused by arrhythmias, valve disorders, cardiomyopathies, cardiac failure, or simply insufficient flow of blood through the cardiac vessels.
Vascular shock
occurs when arterioles lose their normal muscular tone and dilate dramatically. It may arise from a variety of causes, and treatments almost always involve fluid replacement and medications, called inotropic or pressor agents, which restore tone to the muscles of the vessels.
Anaphylactic shock
is a severe allergic response that causes the widespread release of histamines, triggering vasodilation throughout the body.
Obstructive shock
, as the name would suggest, occurs when a significant portion of the vascular system is blocked. It is not always recognized as a distinct condition and may be grouped with cardiogenic shock, including pulmonary embolism and cardiac tamponade. Treatments depend upon the underlying cause and, in addition to administering fluids intravenously, often include the administration of anticoagulants, removal of fluid from the pericardial cavity, or air from the thoracic cavity, and surgery as required. The most common cause is a pulmonary embolism. Other causes include stenosis of the aortic valve; cardiac tamponade; and a pneumothorax
(Betts, et al., 2021)
.
Blood Disorders
Erythrocyte Disorders
Changes in the levels of RBCs can have significant effects on the body’s ability to effectively deliver oxygen to the tissues
(Betts, et al., 2021)
.
Did You Know?
Did you know?
‘O2 sat’ or ‘percent sat’ is the percent saturation; that is, the percentage of hemoglobin sites occupied by oxygen in a patient’s blood.
Anemia
The size, shape, and number of erythrocytes, and the number of hemoglobin molecules can have a major impact on a person’s health. When the number of RBCs or hemoglobin is deficient, the general condition is called
anemia
. There are more than 400 types of anemia.
Anemia can be broken down into three major groups: those caused by blood loss, those caused by faulty or decreased RBC production, and those caused by excessive destruction of RBCs. In addition to these causes, various disease processes also can lead to anemias. These include chronic kidney diseases often associated with a decreased production of EPO, hypothyroidism, some forms of cancer, lupus, and rheumatoid arthritis
(Betts, et al., 2021)
.
Blood Loss Anemias
:
Causes:
Bleeding from wounds or other lesions, including ulcers, hemorrhoids, inflammation of the stomach (gastritis), and some cancers of the gastrointestinal tract
The excessive use of aspirin or other nonsteroidal anti-inflammatory drugs such as ibuprofen can trigger ulceration and gastritis
Excessive menstruation and loss of blood during childbirth.
Anemias Caused by Faulty or Decreased RBC Production:
Sickle cell anemia
Figure 10.14 Sickle Cell Disease. (credit: NIH Image Gallery). From Flickr. Licensed under CC BY-NC 2.0.
A genetic disorder involving the production of an abnormal type of hemoglobin which delivers less oxygen to tissues and causes erythrocytes to assume a sickle (or crescent) shape. See Figure 10.14.
Iron deficiency anemia
The most common type of anemia and results when the amount of available iron is insufficient to allow production of sufficient heme.
Vitamin deficiency anemia
(Generally insufficient vitamin B12 and folate).
Megaloblastic anemia
involves a deficiency of vitamin B12 and/or folate, often due to inadequate dietary intake.
Pernicious anemia
is caused by poor absorption of vitamin B12 and is often seen in patients with Crohn's disease, surgical removal of the intestines or stomach (common in some weight loss surgeries), intestinal parasites, and AIDS.
Aplastic anemia
is the condition in which myeloid stem cells are defective or replaced by cancer cells, resulting in insufficient quantities of RBCs being produced. This condition by be inherited, or it may be triggered by radiation, medication, chemotherapy, or infection.
Thalassemia
is an inherited condition typically occurring in individuals from the Middle East, the Mediterranean, African, and Southeast Asia, in which maturation of the RBCs does not proceed normally. The most severe form is called Cooley’s anemia
(Betts, et al., 2021).
Polycythemia
Polycythemia
is an elevated RBC count and is detected in a patient’s elevated hematocrit. It can occur transiently in a person who is dehydrated; when water intake is inadequate or water losses are excessive, the plasma volume falls. As a result, the hematocrit rises. A mild form of polycythemia is chronic but normal in people living at high altitudes. Some elite athletes train at high elevations specifically to induce this phenomenon. Finally, a type of bone marrow disease called polycythemia vera causes an excessive production of immature erythrocytes. Polycythemia vera can dangerously elevate the viscosity of blood, raising blood pressure and making it more difficult for the heart to pump blood throughout the body. It is a relatively rare disease that occurs more often in men than women, and is more likely to be present in elderly patients those over 60 years of age
(Betts, et al., 2021)
.
Platelet Disorders/Clotting Disorders
Thrombocytosis
Thrombocytosis
is a condition in which there are too many platelets. This may trigger thrombosis, a potentially fatal disorder. A
thrombus
(plural = thrombi) is an aggregation of platelets, erythrocytes, and even WBCs typically trapped within a mass of fibrin strands. While the formation of a clot is a normal step in hemostasis, thrombi can form within an intact or only slightly damaged blood vessel, adhering to the vessel wall and decreasing or obstructing the flow of blood.
(Betts, et al., 2021)
.
Thrombophilia
Thrombophilia, also called hypercoagulation, is a condition in which there is a tendency to form thrombosis. This may be an inherited disorder or may be caused by other conditions including lupus, immune reactions to heparin, polycythemia vera, thrombocytosis, sickle cell disease, pregnancy, and even obesity.
When a portion of a thrombus breaks free from the vessel wall and enters the circulation, it is referred to as an
embolus
. An embolus that is carried through the bloodstream can be large enough to block a vessel critical to a major organ. When it becomes trapped, an embolus is called an
embolism
. In the heart, brain, or lungs, an embolism may accordingly cause a heart attack, a stroke, or a pulmonary embolism
(Betts, et al., 2021)
.
Thrombocytopenia
Thrombocytopenia
is a condition in which there is an insufficient number of platelets, possibly leading to ineffective blood clotting and excessive bleeding
(Betts, et al., 2021)
.
Hemophilia
Hemophilia
is a group of related genetic disorders in which certain plasma clotting factors are lacking or inadequate or nonfunctional. Patients with hemophilia bleed from even minor internal and external wounds, and leak blood into joint spaces after exercise and into urine and stool. Regular infusions of clotting factors isolated from healthy donors can help prevent bleeding in hemophiliac patients. At some point, genetic therapy will become a viable option
(Betts, et al., 2021)
.
Leukocyte Disorders
Leukopenia
Leukopenia
is a condition in which too few leukocytes are produced. If this condition is pronounced, the individual may be unable to ward off disease
(Betts, et al., 2021)
.
Leukocytosis
Leukocytosis
is excessive leukocyte proliferation. Although leukocyte counts are high, the cells themselves are often nonfunctional, leaving the individual at increased risk for disease
(Betts, et al., 2021)
.
Leukemia
Leukemia
is a cancer involving an abundance of leukocytes. It may involve only one specific type of leukocyte from either the myeloid line (myelocytic leukemia) or the lymphoid line (lymphocytic leukemia).  In acute leukemia, there is an overproduction of young, immature leukocytes. In both conditions the cells do not function properly
(Betts, et al., 2021)
.
Lymphoma
Lymphoma
is a form of cancer in which masses of malignant T and/or B lymphocytes collect in lymph nodes, the spleen, the liver, and other tissues. As in leukemia, the malignant leukocytes do not function properly, and the patient is vulnerable to infection. Some forms of lymphoma tend to progress slowly and respond well to treatment. Others tend to progress quickly and require aggressive treatment, without which they are rapidly fatal
(Betts, et al., 2021)
.
Other Conditions Related to Abnormal Leukocyte Counts
Table 10.4. Conditions Related to Abnormal White Blood Cell Counts.
From Betts, et al., 2021. Licensed under
CC BY 4.0.
CELL TYPE
CONDITIONS RELATED TO HIGH COUNTS
CONDITIONS RELATED TO LOW COUNTS
Neutrophil
Infection, inflammation, burns, unusual stress
Drug toxicity, other disorders
Eosinophil
Allergies, parasitic worm infestations, some autoimmune diseases
Drug toxicity, stress
Basophil
Allergies, parasitic infections, hypothyroidism
Pregnancy, stress, hyperthyroidism
Lymphocyte
Viral infections, some cancers
chronic illness, immunosuppression (due to HIV or steroid therapy)
Monocyte
Viral or fungal infections, tuberculosis, some forms of leukemia, other chronic diseases
Bone marrow suppression
Bone Marrow Biopsy/Bone Marrow Transplant
Sometimes, a healthcare provider will order a
bone marrow biopsy
, a diagnostic test of a sample of red bone marrow, or a
bone marrow transplant
, a treatment in which a donor’s healthy bone marrow—and its stem cells—replaces the faulty bone marrow of a patient. These tests and procedures are often used to assist in the diagnosis and treatment of various severe forms of anemia, such as thalassemia major and sickle cell anemia, as well as some types of cancer, specifically leukemia.
In the past, bone marrow sampling or transplant was very painful, as the procedure involved inserting a large-bore needle into the region near the iliac crest of the pelvic bones. Now, direct sampling of bone marrow can often be avoided as stem cells can be isolated in just a few hours from a sample of a patient’s blood. The isolated stem cells are then grown in culture using the appropriate hemopoietic growth factors, and analyzed or sometimes frozen for later use.
For an individual requiring a transplant, a matching donor is essential to prevent the immune system from destroying the donor cells—a phenomenon known as tissue rejection. To treat patients with bone marrow transplants, it is first necessary to destroy the patient’s own diseased marrow through radiation and/or chemotherapy. Donor bone marrow stem cells are then infused into the recipient’s bloodstream, so that they can establish themselves in the recipient’s bone marrow
(Betts, et al., 2021)
.
Common Cardiovascular System – Blood, Abbreviations
Many terms and phrases related to the cardiovascular system – blood are abbreviated. Learn these common abbreviations by expanding the list below.
Query \(\PageIndex{4}\)
Medical Terms in Context
Query \(\PageIndex{5}\)
Medical Specialties and Procedures Related to the Blood Vessels and Blood
Vascular Surgeons
Vascular surgery is a specialty in which the physician treats diseases of the blood and lymphatic vessels. This includes repair and replacement of diseased or damaged vessels, removal of plaque from vessels, minimally invasive procedures including the insertion of venous catheters, and traditional surgery
(Betts, et al., 2021; Society for Vascular Surgery, n.d.)
. For more information, please visit
Society for Vascular Surgery website.
Hematologists
Hematologists are specialist physicians that diagnose and treat blood disorders. These physicians must be well-versed in a wide array of laboratory procedures, basic medical disciplines, and clinical medicine (American Medical Association, 2019). To learn more about hematologists, visit the
American Medical Association’s specialty profile on hematology
Vascular Sonographer
Vascular sonography is a challenging yet rewarding profession. As a sonographer working in this field, you’ll use ultrasound machines to produce images of patients’ veins and arteries using high-frequency sound waves. To learn more, visit the
Vascular Sonography Credentials web page.
 When more than a few drops of blood are required, phlebotomists perform a venipuncture, typically of a surface vein in the arm.  An arterial stick is collected from an artery and used to analyze blood gases. After collection, the blood may be analyzed by medical laboratories or perhaps used for transfusions, donations, or research
(Betts, et al., 2021)
.
Medical Laboratory Scientist/Technician
Medical or clinical laboratories employ a variety of individuals in technical positions. Training is provided through a variety of institutions and certification is through the Canadian Society for Medical Laboratory Science. Specialized positions are:
Medical technologist (MT) tests and analyzes blood, other body fluids, and tissue samples.
Medical laboratory scientists (MLS) perform complex analyses of tissue, blood, and other body fluids.
Medical laboratory assistants (MLA) spend the majority of their time receiving, preparing, testing, and processing specimen samples (American Society for Clinical Pathology, n.d.)


7.11: Global Context
Although Charlemagne possessed one of the most powerful armies in Europe, the Mediterranean, and the Middle East, his empire was hardly a state compared to Tang China, the Abbasid Caliphate, or the Byzantine Empire. Compared to the armies of the Byzantine Emperors, the Abbasid Caliphs, and above all, the Tang emperors, Charlemagne’s army was merely a very large war band, financed not by a state with a working system of taxation and treasury, but rather by the plunder of defeated enemies. Although he issued decrees known as capitularies through the agencies of Church and state, the realm had little in the way of either bureaucracy or infrastructure, save for the decaying network of the Roman Empire’s roads. Indeed, although Charlemagne had sought to have a canal dug between the Rhine and Danube rivers, this project failed—a fitting illustration of the gap between the ambitions of Charlemagne and the reality.
The Carolingian Renaissance
In those territories that had been part of the Western Roman Empire, most of the people had spoken Latin, and Latin was the language of literature. By the time of the Carolingians, Latin was starting to change into the languages that would eventually become French, Spanish, Italian, and Portuguese, languages that we call Romance because they are descended from Latin, the language of the Romans. The Bible, the liturgy, and writings of theology and on saints, however, were still in Latin, although the skill in reading and writing Latin possessed by what few people remained literate had decreased, and in a less literate society, there were fewer books of Roman literature available in Western Europe. The copying of books had gradually dwindled with literacy.
The Carolingians were known not only for their conquests and attempted revival of the Roman Empire, but also for their efforts to improve the state of learning in the Carolingian Empire, particularly with respect to the Bible, theology, and literature of Ancient Rome. They also sought to increase the number of schools and books in the realm. Historians refer to this effort as the Carolingian Renaissance . Historians call it the Carolingian Renaissance in order to distinguish it from the later Italian Renaissance, an effort by northern Italian intellectuals of the fourteenth and fifteenth centuries to restore teaching and learning of the literature of Ancient Greece and Rome.
Charlemagne and his successors sponsored an increase in learning by the Church in order to promote moral reform. Charlemagne, like his predecessors and successors, considered himself a defender and protector of the Christian religion. As such, he wanted to make sure that the Church was promoting a reform of morality. Moral reform would need to start with clergy, and these clergy would need to be able to adequately read the text of the Bible and of the writings of other churchmen (and –women).
Charlemagne’s efforts would be centered on schools and centers of book production, what scholars of medieval Europe call scriptoria (singular scriptorium ). He had help in that there were already many high quality schools attached to monasteries that had been founded in his empire by English and Irish monks. The main school of his empire was the school in his palace at Aachen. His palace itself was based on Roman and Byzantine architecture, as a demonstration that he possessed the same sort of legitimacy as the Roman Emperors. He then invited some of the best scholars of Western Europe to his court—including Alcuin of York (735 – 804), a monk from England—in order both to supervise his own court school and to direct the Church of the Frankish Empire to improve learning.
This improvement of learning included the establishment of new cathedral schools, schools attached to a cathedral church (i.e., a church where the bishop of a diocese—the basic geographic division of the Church—has his seat). These schools trained not only men and women from the church, but also the children of Frankish aristocrats, and in some cases women as well as men. As a result, an increasing number of Frankish nobles would be literate or at least would sponsor efforts by schools to further train people.
Likewise, under the guidance of Charlemagne and the Frankish church, scriptoria throughout his empire launched on a massive new effort to copy new books. Many of these books were religious in character, although Carolingian monks (and nuns) would also copy books from Ancient Rome that had been written by pagans; many of these ancient books, like the poetry of Virgil (see Chapter Six), would serve as the basis of the curriculum of Western Europe’s schools as they had since the Roman Empire. A Christian of the eighth century would believe that even works by pagans would nevertheless afford their readers education and, thus, self-improvement.
The Macedonian Renaissance
The Byzantine Empire had been that half of the Roman Empire where the language of life and culture was not Latin, but Greek. At around the same time as the Carolingians’ efforts, the Byzantine Empire also saw close cooperation of Church and State to revive the study of ancient literature and improve learning. The Byzantine Empire had suffered from a collapse of literacy, which, while not as severe as Western Europe’s, had still resulted in a much less literate population. As such, an effort similar to that of the Carolingians was necessary in the Greek-speaking Eastern Mediterranean. We call this effort the Macedonian Renaissance because it reached its fullest expression under a dynasty of Byzantine emperors that we call the Macedonian Dynasty (867 – 1056).
The efforts of the Macedonian Dynasty, however, had begun earlier. The efforts to improve the availability of books and to increase learning began during the Iconoclast Controversy as both Iconophiles and Iconoclasts had sought to back up their positions by quoting from the Bible and the Church Fathers. Emperor Theophilus (r. 829 – 842), one of the last Iconoclast emperors, had had Leo the Mathematician found a school in the emperor’s palace in Constantinople, a palace known as the Magnaura . Like Charlemagne’s palace at Aachen, this school would go on to serve as the foundation for a revived learning among elites, only this learning was in Greek, rather than Latin.
Following the final triumph of the Iconophiles, these efforts continued with Photius, patriarch of Constantinople from 858 to 867 and then from 877 to 886, as a particular sponsor of monastic schools in the Byzantine Empire and of the copying of books in Ancient Greek, particularly works like those of Plato’s philosophy and the epic poetry of Homer.
Comparisons with the Abbasids
We should also note the global context of both the Carolingian and the Macedonian Renaissance. Carolingian and Macedonian Emperors were not the only ones seeking to increase the availability of ancient texts from the time of the Greeks and Romans. The Abbasid Caliphs under al-Mamun (r. 813 – 883) and his successors also sponsored the work of the House of Wisdom, whose scholars translated the philosophy of the Ancient Greeks into Arabic. Like the Christians of the Carolingian and Byzantine Empires, the Muslims of the Caliphate believed that one could learn from pagan writers even if they had not believed in the one Creator God.


3.1: Describe the role of an online instructor
As you have already learned, when you join an online course, you become part of what is known as a Community of Inquiry and you take on an important role in this online learning environment.
What is the role of your instructor in this learning environment? Your online instructor provides the teaching presence to create design significant learning experiences for you and your fellow students. Instructors also thoughtfully facilitate the content that will support your learning in the class. They also direct you by answering questions and challenging your assumptions to help you grow in your knowledge and skills.
In online classrooms, your instructor takes on the following roles:
- Designer: In a museum, a curator locates the best artifacts to create an effective experience for those who visit. In an online learning environment, your instructors take on the role like that of a curator as they design the course. They will guide you towards readings and other learning materials that will serve your learning goals. Based on their experience in their field, they are able to help you focus your attention on learning resources that are accurate and relevant.
- Facilitator: Your instructor carefully creates opportunities for you to learn the skills you need for your future career, and designs assignments and learning activities to lead you towards intellectual, personal, and professional growth. As you review the course presentation, consider each of the learning activities and assignments. Think about the reasons why your instructor may have selected these course components to contribute to your development.
- Director: Online instructors are available to answer questions along the way. As you learn, you will inevitably find areas that are unclear to you, either related to the course content or your learning process. By communicating with your instructor effectively, you will take full advantage of their role in guiding you on your journey. [1]
For Reflection
Now that you have considered the roles of your online instructor, consider how these roles will shape your work as a student, and your relationship with the instructor.
Click here to download a PDF copy of this worksheet.
| Instructor Role | My Response and Learning Strategies |
| Designer |
|
| Facilitator |
|
| Director |
|
Media Attributions
- Community of Inquiry by Rawia Inaim © CC BY-SA (Attribution ShareAlike)
- Online Instructor Roles by Christina Page © CC BY-SA (Attribution ShareAlike)
-
Garrison, D. R., & Vaughan, N. D. (2008).
Blended learning in higher education: framework, principles, and guidelines
(1st ed). San Francisco: Jossey-Bass.
↵


2.10: Nervous Symptoms Are Unseen
Nervous symptoms seem catastrophic to the person experiencing them, even if the audience may never register their existence. What about trembling hands and knees? Squeaky voice? Dry mouth? Rapid heartbeat? Speakers have a tendency to feel like freaks of nature and that everyone watching thinks the same. Of course, this only occurs because all these symptoms happen to the speaker. However, in reality, the vast majority of nervous symptoms tend to go completely unseen by the audience. Unless a particular audience member shares a close proximity with the speaker, then odds are, the audience spends most of their time directing their focus on listening to the message. After all, few people (if any) participating as audience members attend speeches with the purpose of seeing if they can detect a speaker’s nervous symptoms.
Often, novice speakers will also apologize for their nerves, feeling as though the audience finds the manifestation of such symptoms distracting. However, apologizing only draws attention to symptoms that may have otherwise gone unnoticed. Additionally, apologizing for nervous behaviors might compound the anxiety and make it worse.
Managing Physical Symptoms
Dry Mouth
- Avoid dairy products, soda, and alcoholic beverages. Don’t smoke before speaking. All these items increase mucus production and might leave a lump in the throat.
- Gently bite the tip of the tongue to trigger salivation.
- Drink room-temperature or warm water. Add a lemon, if available.
For Sweaty Hands
- Apply talcum powder or corn starch on hands/body.
- Carry a handkerchief.
Red Splotches on the Face
- Wear pink or red colors.
- Wear high necklines.
- Use humor to release endorphins.
Trembling Voice
- Project voice to the back row of the audience.
Shaky Hands
- Use gestures, but make them small; don’t wave about wildly.
Shaky Legs/Knocking Knees
- Move around gently and easily, but do not pace.
Rapid Heartbeat
- Engage in deep breathing.
- Avoid caffeine and nicotine.


45.5D: Ecological Succession
- Distinguish between primary and secondary succession following disturbances to communities
Community dynamics
Community dynamics are the changes in community structure and composition over time. Sometimes these changes are induced by environmental disturbances such as volcanoes, earthquakes, storms, fires, and climate change. Communities with a stable structure are said to be at equilibrium. Following a disturbance, the community may or may not return to the equilibrium state.
Succession describes the sequential appearance and disappearance of species in a community over time. In primary succession, newly-exposed or newly-formed land is colonized by living things. In secondary succession, part of an ecosystem is disturbed, but remnants of the previous community remain.
Primary succession and pioneer species
Primary succession occurs when new land is formed or rock is exposed; for example, following the eruption of volcanoes, such as those on the Big Island of Hawaii. As lava flows into the ocean, new land is continually being formed. On the Big Island, approximately 32 acres of land are added each year. First, weathering and other natural forces break down the substrate enough for the establishment of certain hearty plants and lichens with few soil requirements, known as pioneer species. These species help to further break down the mineral-rich lava into soil where other, less-hardy species will grow, eventually replacing the pioneer species. In addition, as these early species grow and die, they add to an ever-growing layer of decomposing organic material, contributing to soil formation. Over time, the area will reach an equilibrium state with a set of organisms quite different from the pioneer species.
Secondary succession
A classic example of secondary succession occurs in oak and hickory forests cleared by wildfire.  Their nutrients, however, are returned to the ground in the form of ash. Thus, even when areas are devoid of life due to severe fires, they will soon be ready for new life to take hold.
Before a wildfire, vegetation is often dominated by tall trees with access to the major plant energy resource: sunlight. Their height gives them access to sunlight while also shading the ground and other low-lying species. After the fire, however, these trees are no longer dominant. Thus, the first plants to grow back are usually annual plants followed, within a few years, by quickly-growing and spreading grasses along with other pioneer species. Due to changes in the environment brought on by the growth of the grasses and other species, over many years, shrubs will emerge along with small pine, oak, and hickory trees. These organisms are called intermediate species. Eventually, over 150 years, the forest will reach its equilibrium point where species composition is no longer changing and resembles the community before the fire. This equilibrium state is referred to as the climax community, which will remain stable until the next disturbance.
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- invasive species. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/invasive_species . License : CC BY-SA: Attribution-ShareAlike
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- camouflage. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/camouflage . License : CC BY-SA: Attribution-ShareAlike
- herbivory. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/herbivory . License : CC BY-SA: Attribution-ShareAlike
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Key Points
- After an environmental disturbance such as a volcanic eruption or forest fire, communities are able to replace lost species through the process of succession.
- Primary succession occurs after a volcanic eruption or earthquake; it involves the breakdown of rocks by lichens to create new, nutrient -rich soils.
- The first species to colonize an area after a major disturbance are called pioneer species; they help to form the new environment.
- Secondary succession occurs after a disturbance such as a forest fire, where there is still some organic matter to allow new plants to grow.
- Both types of succession take place over long periods of time and result in the communities reaching a state of equilibrium.
Key Terms
- succession : an act of following in sequence
- equilibrium : the condition of a system in which competing influences are balanced, resulting in no net change


8.0: Fitting Linear Models to Data
In this section, you will:
- Draw and interpret scatter plots.
- Find the line of best fit.
- Distinguish between linear and nonlinear relations.
- Use a linear model to make predictions.
A professor is attempting to identify trends among final exam scores. His class has a mixture of students, so he wonders if there is any relationship between age and final exam scores. One way for him to analyze the scores is by creating a diagram that relates the age of each student to the exam score received. In this section, we will examine one such diagram known as a scatter plot.
Drawing and Interpreting Scatter Plots
A scatter plot is a graph of plotted points that may show a relationship between two sets of data. If the relationship is from a linear model , or a model that is nearly linear, the professor can draw conclusions using his knowledge of linear functions. Figure 1 shows a sample scatter plot.
Notice this scatter plot does not indicate a linear relationship . The points do not appear to follow a trend. In other words, there does not appear to be a relationship between the age of the student and the score on the final exam.
Example 1
Using a Scatter Plot to Investigate Cricket Chirps
Table 1 shows the number of cricket chirps in 15 seconds, for several different air temperatures, in degrees Fahrenheit 5 . Plot this data, and determine whether the data appears to be linearly related.
| Chirps | 44 | 35 | 20.4 | 33 | 31 | 35 | 18.5 | 37 | 26 |
| Temperature | 80.5 | 70.5 | 57 | 66 | 68 | 72 | 52 | 73.5 | 53 |
- Answer
-
Plotting this data, as depicted in Figure 2 suggests that there may be a trend. We can see from the trend in the data that the number of chirps increases as the temperature increases. The trend appears to be roughly linear, though certainly not perfectly so.
Finding the Line of Best Fit
Once we recognize a need for a linear function to model that data, the natural follow-up question is “what is that linear function?” One way to approximate our linear function is to sketch the line that seems to best fit the data. Then we can extend the line until we can verify the y -intercept. We can approximate the slope of the line by extending it until we can estimate the
Example 2
Finding a Line of Best Fit
Find a linear function that fits the data in Table 1 by “eyeballing” a line that seems to fit.
- Answer
-
On a graph, we could try sketching a line.
Using the starting and ending points of our hand drawn line, points (0, 30) and (50, 90), this graph has a slope of
and a y -intercept at 30. This gives an equation of
where is the number of chirps in 15 seconds, and is the temperature in degrees Fahrenheit. The resulting equation is represented in Figure 3 .
Analysis
This linear equation can then be used to approximate answers to various questions we might ask about the trend.
Recognizing Interpolation or Extrapolation
While the data for most examples does not fall perfectly on the line, the equation is our best guess as to how the relationship will behave outside of the values for which we have data. We use a process known as interpolation when we predict a value inside the domain and range of the data. The process of extrapolation is used when we predict a value outside the domain and range of the data.
Figure 4 compares the two processes for the cricket-chirp data addressed in Example 2 . We can see that interpolation would occur if we used our model to predict temperature when the values for chirps are between 18.5 and 44. Extrapolation would occur if we used our model to predict temperature when the values for chirps are less than 18.5 or greater than 44.
There is a difference between making predictions inside the domain and range of values for which we have data and outside that domain and range. Predicting a value outside of the domain and range has its limitations. When our model no longer applies after a certain point, it is sometimes called model breakdown . For example, predicting a cost function for a period of two years may involve examining the data where the input is the time in years and the output is the cost. But if we try to extrapolate a cost when that is in 50 years, the model would not apply because we could not account for factors fifty years in the future.
Interpolation and Extrapolation
Different methods of making predictions are used to analyze data.
- The method of interpolation involves predicting a value inside the domain and/or range of the data.
- The method of extrapolation involves predicting a value outside the domain and/or range of the data.
- Model breakdown occurs at the point when the model no longer applies.
Example 3
Understanding Interpolation and Extrapolation
Use the cricket data from Table 1 to answer the following questions:
- ⓐ Would predicting the temperature when crickets are chirping 30 times in 15 seconds be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.
- ⓑ Would predicting the number of chirps crickets will make at 40 degrees be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.
- Answer
-
-
ⓐ
The number of chirps in the data provided varied from 18.5 to 44. A prediction at 30 chirps per 15 seconds is inside the domain of our data, so would be interpolation. Using our model:
Based on the data we have, this value seems reasonable. -
ⓑ
The temperature values varied from 52 to 80.5. Predicting the number of chirps at 40 degrees is extrapolation because 40 is outside the range of our data. Using our model:
We can compare the regions of interpolation and extrapolation using Figure 5 .
-
ⓐ
The number of chirps in the data provided varied from 18.5 to 44. A prediction at 30 chirps per 15 seconds is inside the domain of our data, so would be interpolation. Using our model:
Analysis
Our model predicts the crickets would chirp 8.33 times in 15 seconds. While this might be possible, we have no reason to believe our model is valid outside the domain and range. In fact, generally crickets stop chirping altogether below around 50 degrees.
Try It #1
According to the data from Table 1 , what temperature can we predict it is if we counted 20 chirps in 15 seconds?
Finding the Line of Best Fit Using a Graphing Utility
While eyeballing a line works reasonably well, there are statistical techniques for fitting a line to data that minimize the differences between the line and data values 6 . One such technique is called least squares regression and can be computed by many graphing calculators, spreadsheet software, statistical software, and many web-based calculators 7 . Least squares regression is one means to determine the line that best fits the data, and here we will refer to this method as linear regression.
How To
Given data of input and corresponding outputs from a linear function, find the best fit line using linear regression.
- Enter the input in List 1 ( L1 ).
- Enter the output in List 2 ( L2 ).
- On a graphing utility, select Linear Regression ( LinReg ).
Example 4
-
On a graphing utility, select Linear Regression (LinReg). Using the cricket chirp data from earlier, with technology we obtain the equation:
Analysis
Notice that this line is quite similar to the equation we “eyeballed” but should fit the data better. Notice also that using this equation would change our prediction for the temperature when hearing 30 chirps in 15 seconds from 66 degrees to:
The graph of the scatter plot with the least squares regression line is shown in Figure 6 .
Q&A
Will there ever be a case where two different lines will serve as the best fit for the data?
No. There is only one best fit line.
Distinguishing Between Linear and Non-Linear Models
As we saw above with the cricket-chirp model, some data exhibit strong linear trends, but other data, like the final exam scores plotted by age, are clearly nonlinear. Most calculators and computer software can also provide us with the correlation coefficient , which is a measure of how closely the line fits the data. Many graphing calculators require the user to turn a ”diagnostic on” selection to find the correlation coefficient, which mathematicians label as The correlation coefficient provides an easy way to get an idea of how close to a line the data falls.
We should compute the correlation coefficient only for data that follows a linear pattern or to determine the degree to which a data set is linear. If the data exhibits a nonlinear pattern, the correlation coefficient for a linear regression is meaningless. To get a sense for the relationship between the value of and the graph of the data, Figure 7 shows some large data sets with their correlation coefficients. Remember, for all plots, the horizontal axis shows the input and the vertical axis shows the output.
Correlation Coefficient
The correlation coefficient is a value, between –1 and 1.
- r > 0 suggests a positive (increasing) relationship
- r < 0 suggests a negative (decreasing) relationship
- The closer the value is to 0, the more scattered the data.
- The closer the value is to 1 or –1, the less scattered the data is.
Example 5
Finding a Correlation Coefficient
Calculate the correlation coefficient for cricket-chirp data in Table 1 .
- Answer
-
Because the data appear to follow a linear pattern, we can use technology to calculate Enter the inputs and corresponding outputs and select the Linear Regression. The calculator will also provide you with the correlation coefficient, This value is very close to 1, which suggests a strong increasing linear relationship.
Note: For some calculators, the Diagnostics must be turned "on" in order to get the correlation coefficient when linear regression is performed: [2nd]>[0]>[alpha][ –1], then scroll to DIAGNOSTICSON .
Predicting with a Regression Line
Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned above, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.
Example 6
Using a Regression Line to Make Predictions
Gasoline consumption in the United States has been steadily increasing. Consumption data from 1994 to 2004 is shown in Table 3 8 . Determine whether the trend is linear, and if so, find a model for the data. Use the model to predict the consumption in 2008.
| Year | '94 | '95 | '96 | '97 | '98 | '99 | '00 | '01 | '02 | '03 | '04 |
| Consumption (billions of gallons) | 113 | 116 | 118 | 119 | 123 | 125 | 126 | 128 | 131 | 133 | 136 |
- Answer
-
We can introduce new input variable, representing years since 1994.
The least squares regression equation is:
Using technology, the correlation coefficient was calculated to be 0.9965, suggesting a very strong increasing linear trend.
Using this to predict consumption in 2008
The model predicts 144.244 billion gallons of gasoline consumption in 2008.
Try It #2
Use the model we created using technology in Example 6 to predict the gas consumption in 2011. Is this an interpolation or an extrapolation?
Access these online resources for additional instruction and practice with fitting linear models to data.


29.2: Using Long Division
Lesson
Let's use long division.
Exercise \(\PageIndex{1}\): Number Talk: Estimating Quotients
Estimate these quotients mentally.
\(500\div 7\)
\(1,394\div 9\)
Exercise \(\PageIndex{2}\): Lin Uses Long Division
Lin has a method of calculating quotients that is different from Elena’s method and Andre’s method. Here is how she found the quotient of \(657\div 3\):
-
Discuss with your partner how Lin’s method is similar to and different from drawing base-ten diagrams or using the partial quotients method.
- Lin subtracted \(3\cdot 2\) then \(3\cdot 1\), and lastly \(3\cdot 9\). Earlier, Andre subtracted \(3\cdot 200\) then \(3\cdot 10\), and lastly \(3\cdot 9\). Why did they have the same quotient?
- In the third step, why do you think Lin wrote the 7 next to the remainder of 2 rather than adding 7 and 2 to get 9?
-
Lin’s method is called
long division
. Use this method to find the following quotients. Check your answer by multiplying it by the divisor.
- \(846\div 3\)
- \(1,816\div 4\)
- \(768\div 12\)
Exercise \(\PageIndex{3}\): Dividing Whole Numbers
- Find each quoteint.
- \(633\div 3\)
- \(1001\div 7\)
- \(2996\div 14\)
- Here is Priya's calculation of \(906\div 3\)
- Priya wrote 320 for the value of \(906\div 3\). Check her answer by multiplying it by 3. What product do you get and what does it tell you about Priya’s answer?
- Describe Priya’s mistake, then show the correct calculation and answer.
Summary
Long division is another method for calculating quotients. It relies on place value to perform and record the division.
When we use long division, we work from left to right and with one digit at a time, starting with the leftmost digit of the dividend. We remove the largest group possible each time, using the placement of the digit to indicate the size of each group. Here is an example of how to find \(948\div 3\) using long division.
- We start by dividing 9 hundreds into 3 groups, which means 3 hundreds in each group. Instead of writing 300, we simply write 3 in the hundreds place, knowing that it means 3 hundreds.
- There are no remaining hundreds, so we work with the tens. We can make 3 groups of 1 ten in 4 tens, so we write 1 in the tens place above the 4 of 948. Subtracting 3 tens from 4 tens, we have a remainder of 1 ten.
- We know that 1 ten is 10 ones. Combining these with the 8 ones from 948, we have 18 ones. We can make 3 groups of 6, so we write 6 in the ones place.
In total, there are 3 groups of 3 hundreds, 1 ten, and 6 ones in 948, so \(948\div 3=316\).
Glossary Entries
Definition: Long Division
Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.
For example, here is the long division for \(57\div 4\).
Practice
Exercise \(\PageIndex{4}\)
Kiran is using long division to find \(696\div 12\).
He starts by dividing 69 by 12. In which decimal place should Kiran place the first digit of the quotient (5)?
- Hundreds
- Tens
- Ones
- Tenths
Exercise \(\PageIndex{5}\)
Here is a long-division calculation of \(917\div 7\).
- There is a 7 under the 9 of 917. What does this 7 represent?
- What does the subtraction of 7 from 9 mean?
- Why is a 1 written next to the 2 from \(9-7\)?
Exercise \(\PageIndex{6}\)
Han's calculation of \(972\div 9\) is shown here.
- Find \(180\cdot 9\).
- Use your calculation of \(180\cdot 9\) to explain how you know Han has made a mistake.
- Identify and correct Han’s mistake.
Exercise \(\PageIndex{7}\)
Find each quotient.
Exercise \(\PageIndex{8}\)
One ounce of a yogurt contains of \(1.2\) grams of sugar. How many grams of sugar are in \(14.25\) ounces of yogurt?
- \(0.171\) grams
- \(1.71\) grams
- \(17.1\) grams
- \(171\) grams
(From Unit 5.3.3)
Exercise \(\PageIndex{9}\)
The mass of one coin is 16.718 grams. The mass of a second coin is 27.22 grams. How much greater is the mass of the second coin than the first? Show your reasoning.
(From Unit 5.2.3)