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 unique. The number defined by a decimal representation is often written more briefly as That is to say, "a" is the integer part of "r", not necessarily between 0 and 9, and "a", "a", "a", ... are the digits forming the fractional part of "r". Both notations above are, by definition, the following limit of a sequence: Any real number can be approximated to any desired degree of accuracy by rational numbers with finite decimal representations. Assume formula_4. Then for every integer formula_5 there is a finite decimal formula_6 such that Proof: Let formula_8, where formula_9. Then formula_10, and the