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
Repeating decimal 9. Knowing just that, a general repeating decimal can be expressed as a fraction without having to solve an equation. For example, one could reason: It is possible to get a general formula expressing a repeating decimal with an "n" digit period (repetend length), beginning right after the decimal point, as a fraction: More explicitly one gets the following cases. If the repeating decimal is between 0 and 1, and the repeating block is "n" digits long, first occurring right after the decimal point, then the fraction (not necessarily reduced) will be the integer number represented by the "n"-digit block