Decimal and, only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called "decimal fractions" or "decimal numbers" for forming the "decimal numeral system". For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot "" in many countries (including English speaking ones),
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