Arabic numerals.docx

Three Arab numeration system based on Hindu numerals replaced much older ciphered Egyptian and Greek numeration systems after 800 CE. The older numeration systems scaled rational number n/p by multiplying by (m/m) to reach (mn/mp) so that the best divisors of denominator (mp) were concisely summed to numerator (mn) in 2-term, 3-term, 4-term and 5-term series. Greeks had mapped numerals onto Ionian and Doric letters and unit fractions by adding (’) to the numerals. 1/2 = to beta’, 1/3 = gamma’. An Egyptian zero, sfr, was used in double-entry accounting to denote empty accounts, and a Greek zero, by two dots over an oval, was used in a range of arithmetic situations. The older unit fraction systems generally scaled rational numbers in a multiplication context from 2050 BCE to 800 AD that were very useful in solving business and science problems in both cultures.