Scalesof Notation

Scales of Notation. We are accustomed to express any number in terms of multiples of ten and its powers; for instance-

7234 = 4 + (3 x 10) + (2 x 10²) + (7 x 10³).

Here 10 is said to be the radix of the scale, which is known as the decimal scale or system. The radix might, however, be any other number, e.g. the number 7234 might be expressed as 30042, the radix being 7; for

4 + 3 x 10 + 2 x 10² + 7 x 10³ = 2 + 4 x 7 + 0 x 7² + 0 x 7³ + 3 x 7⁴.

The use of the decimal system is very general, the choice of ten as the radix being probably suggested by the number of fingers, but other systems have been in vogue. [NOTATION.] The duodecimal system (radix 12) leaves some signs of its existence in the foot (12 inches), the shilling (12 pence), etc.