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 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