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
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