Decimal numbers that may be expressed as a fraction, the denominator of which is a power of ten. For example, the numerals formula_5 represent the fractions , , . More generally, a decimal with digits after the separator represents the fraction with denominator , whose numerator is the integer obtained by removing the separator. Expressed as a fully reduced fraction, the decimal numbers are those, whose denominator is a product of a power of 2 by a power of 5. Thus the smallest denominators of decimal numbers are The "integer part", or "integral part" of a decimal is the integer written
Decimal do not allow an exact representation for all real numbers, so e.g. for the real number . Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates the real , being less than 10 off; and so decimals are widely used in science, engineering and everyday life. More precisely, for every real number "x", and every positive integer "n", there are two decimals "l" and "u", with at most "n" digits after the decimal mark, such that "l" ≤ "x" ≤ "u" and ("u" – "l") = 10. Numbers are very often obtained as