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),
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" =