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 (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.