Decimal the Roman numerals did, an intermediate base of 5. Notably, the polymath Archimedes (ca. 287–212 BC) invented a decimal positional system in his Sand Reckoner which was based on 10 and later led the German mathematician Carl Friedrich Gauss to lament what heights science would have already reached in his days if Archimedes had fully realized the potential of his ingenious discovery. The Hittites hieroglyphs (since 15th century BC), just like the Egyptian and early numerals in Greece, was strictly decimal. Some non-mathematical ancient texts like the Vedas dating back to 1900–1700 BCE make use of decimals and mathematical decimal
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" =