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===Ancient Near East=== {| style="float:right; clear:right; text-align:center; border: 1px solid" align=right cellspacing=0 cellpadding=8 |- !nfr<br /> |heart with [[trachea]]<br />beautiful, pleasant, good |<hiero>F35</hiero> |} Ancient [[Egyptian numerals]] were of [[decimal|base 10]].<ref>{{Cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |date=2000 |title=Egyptian numerals |url=http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html |url-status=live |archive-url=https://web.archive.org/web/20191115221313/http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html |archive-date=15 November 2019 |access-date=21 December 2019 |website=[[mathshistory.st-andrews.ac.uk]] |publisher=University of St Andrews}}</ref> They used [[hieroglyphs]] for the digits and were not [[positional notation|positional]]. In [[Papyrus Boulaq 18|one papyrus]] written around {{nowrap|1770 BC}}, a scribe recorded daily incomes and expenditures for the [[pharaoh]]'s court, using the ''[[Nefer|nfr]]'' hieroglyph to indicate cases where the amount of a foodstuff received was exactly equal to the amount disbursed. Egyptologist [[Alan Gardiner]] suggested that the ''nfr'' hieroglyph was being used as a symbol for zero. The same symbol was also used to indicate the base level in drawings of tombs and pyramids, and distances were measured relative to the base line as being above or below this line.<ref>{{cite journal|first=Beatrice |last=Lumpkin |doi=10.1007/BF03024613 |title=Mathematics Used in Egyptian Construction and Bookkeeping |journal=The Mathematical Intelligencer |year=2002 |volume=24 |number=2 |pages=20–25|s2cid=120648746 }}</ref> By the middle of the 2nd millennium BC, [[Babylonian mathematics]] had a sophisticated [[sexagesimal|base 60]] positional numeral system. The lack of a positional value (or zero) was indicated by a ''space'' between [[sexagesimal]] numerals. In a tablet unearthed at [[Kish (Sumer)|Kish]] (dating to as early as {{nowrap|700 BC}}), the scribe Bêl-bân-aplu used three hooks as a [[Free variables and bound variables|placeholder]] in the same [[Babylonian numerals|Babylonian system]].{{sfn|Kaplan|2000}} By {{nowrap|300 BC}}, a punctuation symbol (two slanted wedges) was repurposed as a placeholder.<ref>{{Cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |date=2000 |title=Zero |url=https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ |url-status=live |archive-url=https://web.archive.org/web/20210921191118/https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ |archive-date=21 September 2021 |access-date=2021-09-07 |website=Maths History |publisher=University of St Andrews |language=en}}</ref><ref>{{Cite web |title=Babylonian mathematics | date= 2016 |url=https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976 |access-date=2021-09-07 |website= The Open University |archive-date=7 September 2021 |archive-url=https://web.archive.org/web/20210907135356/https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976 |url-status=live }}</ref> The Babylonian positional numeral system differed from the later [[Hindu–Arabic numeral system|Hindu–Arabic system]] in that it did not explicitly specify the magnitude of the leading sexagesimal digit, so that for example the lone digit 1 ([[File:Babylonian 1.svg|20px]]) might represent any of 1, 60, 3600 = 60<sup>2</sup>, etc., similar to the significand of a [[floating-point number]] but without an explicit exponent, and so only distinguished implicitly from context. The zero-like placeholder mark was only ever used in between digits, but never alone or at the end of a number.{{sfn|Reimer|2014|p=172}}
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