A special case of division to be considered is the determination of the
_reciprocal_ of a number _n_, or (1)/(_n_). Following the ordinary rule
for division, it is evident that setting _n_ on C to 1 on D, gives
(1)/(_n_) on D under 1 on C. It is more important to observe that by
inverting the operation—setting 1 (or 10) on C to _n_ on D—we can read
(1)/(_n_) on C over 1 (or 10) on D. Hence whenever a result is read on D
under an index of C, we can also read its reciprocal on C over whichever
index of D is available.
_The Number of Digits in a Reciprocal_ is obvious when _n_ = 10, 100, or
any power (_p_) of 10. Thus (1)/(10) = 0·1; (1)/(100) = 0·01;
(1)/(10^{_p_}) = 1 preceded by _p_ − 1 cyphers. For all other cases we
have the rule:—_Subtract from 1 the number of digits in the number._