The slide rule

A convenient method of representing an arithmetical quantity is to split it up into two factors, of which the first is the original number, with the decimal point moved so as to immediately follow the first significant figure, and the second, 10ⁿ where n is the number of places the decimal point has been moved, this index being positive for numbers greater than 1, and negative for numbers less than 1.^[1] In this system, therefore, we regard 3,610,000 as 3·61 × 1,000,000, and write it as 3·61 × 10⁶. Similarly 361 = 3·61 x 10²; 0·0361 (= 3·61
100) = 3·61 × 10⁻²; 0·0000361 = 3·61 × 10⁻⁵, etc. To restore a number to its original form, we have only to move the decimal point through the number of places indicated by the index, moving to the right if the index is positive and to the left (prefixing 0’s) if negative. This method, which should be cultivated for ordinary arithmetical work, is substantially that followed in calculating by the slide rule. Thus with the slide rule the multiplication of 63,200 by 0·0035 virtually resolves itself into 6·32 × 10⁴ × 3·5 × 10⁻³ or 6·32 × 3·5 × 10^4–3 = 22·12 x 10¹ = 221·2. It will be seen later, however, that the result can be arrived at by a more direct, if less systematic, method of working.