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 do not allow an exact representation for all real numbers, so e.g. for the real number . Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates the real , being less than 10 off; and so decimals are widely used in science, engineering and everyday life. More precisely, for every real number "x", and every positive integer "n", there are two decimals "l" and "u", with at most "n" digits after the decimal mark, such that "l" ≤ "x" ≤ "u" and ("u" – "l") = 10. Numbers are very often obtained as