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 (base 12) is 12 (base 10), 10^2 (base 12) is 144 (base 10), 21 (base 12) is 25 (base 10), ᘔ5 (base 12) is 125 (base 10), ... Repeating decimals (also called decimal sequences) have found cryptographic and error-correction coding applications. In these applications repeating decimals to base 2 are generally used which gives rise to binary sequences. The maximum length binary sequence for 1/"p" (when 2 is a primitive root of "p") is given by: These sequences of period "p" − 1 have an autocorrelation function that has a negative peak of −1 for shift of ("p" − 1)/2.