Decimal
- c. 3500 - 2500 BC Elamites of Iran possibly used early forms of decimal system. [2] [3]
- c. 2900 BC Egyptian hieroglyphs show counting in powers of 10 (1 million + 400,000 goats, etc.) – see Ifrah, below
- c. 2600 BC Indus Valley Civilization, earliest known physical use of decimal fractions in ancient weight system: 1/20, 1/10, 1/5, 1/2. See Ancient Indus Valley weights and measures
- c. 1400 BC Chinese writers show familiarity with the concept: for example, 547 is written 'Five hundred plus four decades plus seven of days' in some manuscripts
- c. 1200 BC In ancient India, the Vedic text Yajur-Veda states the powers of 10, up to 1055
- c. 400 BC Pingala – develops the binary number system for Sanskrit prosody, with a clear mapping to the base-10 decimal system
- c. 250 BC Archimedes writes the Sand Reckoner, which takes decimal calculation up to 1080,000,000,000,000,000
- c. 100–200 The Satkhandagama written in India – earliest use of decimal logarithms
- c. 476–550 Aryabhata – uses an alphabetic cipher system for numbers that used zero
- c. 598–670 Brahmagupta – explains the Hindu-Arabic numerals (modern number system) which uses decimal integers, negative integers, and zero
- c. 780–850 Muḥammad ibn Mūsā al-Ḵwārizmī – first to expound on algorism outside India
- c. 920–980 Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi – earliest known direct mathematical treatment of decimal fractions.
- c. 1300–1500 The Kerala School in South India – decimal floating point numbers
- 1548/49–1620 Simon Stevin – author of De Thiende ('the tenth')
- 1561–1613 Bartholemaeus Pitiscus – (possibly) decimal point notation.
- 1550–1617 John Napier – use of decimal logarithms as a computational tool
- 1765 Johann Heinrich Lambert – discusses (with few if any proofs) patterns in decimal expansions of rational numbers and notes a connection with Fermat's little theorem in the case of prime denominators
- 1800 Karl Friedrich Gauss – uses number theory to systematically explain patterns in recurring decimal expansions of rational numbers (e.g., the relation between period length of the recurring part and the denominator, which fractions with the same denominator have recurring decimal parts which are shifts of each other, like 1/7 and 2/7) and also poses questions which remain open to this day (e.g., a special case of Artin's conjecture on primitive roots: is 10 a generator modulo p for infinitely many primes p?).
- 1925 Louis Charles Karpinski – The History of Arithmetic [1]
- 1959 Werner Buchholz – Fingers or Fists? (The Choice of Decimal or Binary representation)[2]
- 1974 Hermann Schmid – Decimal Computation[3]
- 2000 Georges Ifrah – The Universal History of Numbers: From Prehistory to the Invention of the Computer[4]
- 2003 Mike Cowlishaw – Decimal Floating-Point: Algorism for Computers[5].
[
Natural languages
A straightforward decimal system, in which 11 is expressed as ten-one and 23 as two-ten-three, is found in Chinese languages except Wu, and in Vietnamese with a few irregularities. Japanese, Korean, and Thai have imported the Chinese decimal system. Many other languages with a decimal system have special words for the numbers between 10 and 20, and decades.
Incan languages such as Quechua and Aymara have an almost straightforward decimal system, in which 11 is expressed as ten with one and 23 as two-ten with three.
Some psychologists suggest irregularities of numerals in a language may hinder children's counting ability[6].
[
See also
[
References
- ^ The History of Arithmetic, Louis Charles Karpinski, 200pp, Rand McNally & Company, 1925.
- ^ Fingers or Fists? (The Choice of Decimal or Binary representation), Werner Buchholz, Communications of the ACM, Vol. 2 #12, pp3–11, ACM Press, December 1959.
- ^ Decimal Computation, Hermann Schmid, John Wiley & Sons 1974 (ISBN 047176180X); reprinted in 1983 by Robert E. Krieger Publishing Company (ISBN 0898743184)
- ^ Histoire universelle des chiffres, Georges Ifrah, Robert Laffont, 1994 (The Universal History of Numbers: From prehistory to the invention of the computer, Georges Ifrah, John Wiley and Sons Inc., 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk)
- ^ Decimal Floating-Point: Algorism for Computers, Cowlishaw, M. F., Proceedings 16th IEEE Symposium on Computer Arithmetic, ISBN 0-7695-1894-X, pp104-111, IEEE Comp. Soc., June 2003
- ^ Azar, Beth (1999), “English words may hinder math skills development”, American Psychology Association Monitor 30 (4), <http://www.apa.org/monitor/apr99/english.html>.
[
External links
- Decimal arithmetic FAQ
- Tests: Decimal Place Value Sums Fractions
- Practice Decimal Arithmetic with Printable Worksheets
- Converting Decimals to Fractions
- Cultural Aspects of Young Children's Mathematics Knowledge
- Decimal Bibliography
For more information review our copyright contact and privacy policy.