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, 10^{_n_} 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 × 10^6. Similarly 361 = 3·61 x 10^2; 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 × 10^4 × 3·5 × 10^{−3} or
6·32 × 3·5 × 10^{4–3} = 22·12 x 10^1 = 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.