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 the successive remainders displayed above are 56, 42, 50. When we arrive at 50 as the remainder, and bring down the "0", we find ourselves dividing 500 by 74, which is the same problem we began with. Therefore, the decimal repeats: 0.0675 675 675 …. For any given divisor, only finitely many different remainders can occur. In the example above, the 74 possible remainders are 0, 1, 2, …, 73. If at any point in the division the remainder is 0, the expansion terminates at that point. If 0 never occurs as a remainder, then the division process continues forever,