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 require the terminating decimal to be negative). For example, It follows that any repeating decimal with period "n", and "k" digits after the decimal point that do not belong to the repeating part, can be written as a (not necessarily reduced) fraction whose denominator is (10 − 1)10. Conversely the period of the repeating decimal of a fraction "c"/"d" will be (at most) the smallest number "n" such that 10 − 1 is divisible by "d". For example, the fraction 2/7 has "d" = 7, and the smallest "k" that makes 10 − 1 divisible by 7 is "k" =