text: who was first in using base ten in arithmetic? did one thousand among the romans mean the samething among semetic people. the modern base ten system uses ten symbols (0, 1, 2, 3, ...,9) with place values that are powers of ten. these symbols are commonly called hindu-arabic numerals. although a base ten system seems natural to those who have ten þngers, in times past people have used many different kinds of numerals and various bases in addition to base ten. other numeration systems that have existed historically used base þve, base twenty, and base sixty. in fact almost all societies have used a number system based on 5, 10, or 20. this is understandable because of human anatomy. counting on the þve þngers of one hand, all ten þngers, or all twenty digits is natural and useful. the quinary system (base 5) or vigesimal (base 20) or a combination of these two were used by early societies in the americas including almost all eskimo tribes, some native north american societies, and almost all peoples indigenous to central and south america. although the quinary and vigesimal systems were also found in some societies in northern siberia and africa the decimal system used today dominated history. however, with advent of computers in this century bases two, eight and sixteen have come into prominence. computers count best using only two digits. it is interesting to note that certain polish engineers built a computer in the late 1950s and early 1960s that used a base of negative 2. in order to understand numeration systems it is important to know the distinction between place value systems and additive systems. in additive systems (roman numerals, for example) a numeration symbol has the same meaning no matter where it is placed in writing the number. so, for example, the roman numeral v means þve whether it is placed before or after the numeral x. thus xv and vx both represent þfteen in an additive system, although as we discover vx would certainly be non-standard. the values ten (x) and þve (v) are added to obtain þfteen. the position of each numeral is important in positional (place value) number systems, but not in additive systems. for example, in order to represent þfty or þve hundred in the base ten place value system, the symbol 5 is moved over to the left one or two places (50 or 500), putting a zero in the empty places. however, in order to represent þfty or þve hundred in an additive system multiple copies of the ten or hundred need to be used (xxxxx or ccccc) or new symbols need to be invented (l and d in roman numerals). place value (or positional) systems can continue to use the same set of symbols since the value of the symbol changes with repositioning. the value of each symbol is multiplied by a power of the systems base. for example, in base ten (decimal) different positions of the numeral þve will represent þve, þfty, and þve hundred. hence, the symbol 5 in each of the following numbers represents different quantities because of its position.  in 215 the þve represents þve (5 × 100 )  in 354 the þve represents þfty (5 × 101 )  in 567 the þve represents þve hundred (5 × 103 ) the number one hundred twenty four is represented as 124 in the base ten system, where the 1 signiþes one hundred, the 2 signiþes two tens and the 4 signiþes four ones. this number is written in expanded form as follows: