<P> Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals and the vigesimal (base 20) system that defined Maya numerals . Because of this place - value concept, the ability to reuse the same digits for different values contributed to simpler and more efficient methods of calculation . </P> <P> The continuous historical development of modern arithmetic starts with the Hellenistic civilization of ancient Greece, although it originated much later than the Babylonian and Egyptian examples . Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs . For example, Nicomachus summarized the viewpoint of the earlier Pythagorean approach to numbers, and their relationships to each other, in his Introduction to Arithmetic . </P> <P> Greek numerals were used by Archimedes, Diophantus and others in a positional notation not very different from ours . The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds . For the thousands place they would reuse the symbols for the units place, and so on . Their addition algorithm was identical to ours, and their multiplication algorithm was only very slightly different . Their long division algorithm was the same, and the digit - by - digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes, who may have invented it . He preferred it to Hero's method of successive approximation because, once computed, a digit doesn't change, and the square roots of perfect squares, such as 7485696, terminate immediately as 2736 . For numbers with a fractional part, such as 546.934, they used negative powers of 60 instead of negative powers of 10 for the fractional part 0.934 . </P> <P> The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra . The ancient Chinese used a positional notation similar to that of the Greeks . Since they also lacked a symbol for zero, they had one set of symbols for the unit's place, and a second set for the ten's place . For the hundred's place they then reused the symbols for the unit's place, and so on . Their symbols were based on the ancient counting rods . It is a complicated question to determine exactly when the Chinese started calculating with positional representation, but it was definitely before 400 BC . The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers as explained in the Nine Chapters on the Mathematical Art (Jiuzhang Suanshu), which was written by Liu Hui . </P>

Basic operations that can be performed on relation