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 representation procedure to formula_32 and denoting the resultant decimal expansion by formula_33. The decimal expansion of non-negative real number "x" will end in zeros (or in nines) if, and only if, "x" is a rational number whose denominator is of the form 25, where "m" and "n" are non-negative integers. Proof: If the decimal expansion of "x" will end in zeros, or formula_34 for some "n", then the denominator of "x" is of the form 10 = 25. Conversely, if the denominator of "x" is of the form 25, formula_35 for some "p". While "x" is of the form formula_36, formula_37