In division, similar modifications are necessary. If when moving the slide to the right the division can be completely effected by using the L.H. scale of A, the quotient (read on A above the L.H. of index B) has a number of digits equal to the number in the dividend, less the number in the divisor, _plus 1_. But if the division necessitates the use of both the A scales, the number of digits in the quotient equals the number in the dividend, less the number in the divisor. RECIPROCALS. 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._ EX.—(1)/(339) = 0·00295. There are 3 digits in the number; hence, there are 1 − 3 = −2 digits in the answer. EX.—(1)/(0·0000156) = 64,100. There are −4 digits in the number; hence, there are 1 − (−4) = 5 digits in the result. CONTINUED MULTIPLICATION AND DIVISION. By combining the rules for multiplication and division, we can readily evaluate expressions of the form (_a_)/(_b_) × (_c_)/(_d_) × (_e_)/(_f_) × (_g_)/(_h_) = _x_. The simplest case, (_a_ × _c_)/(_b_) can be solved by one setting of the slide.[3] Take as an example, (14·45 × 60)/(8·5) = 102. Setting 8·5 on C to 14·45 on D, we can, if desired, read 1·7 on D under 1 on C, as the quotient. However, we are not concerned with this, but require its multiplication by 60, and the slide being already set for this operation, we at once read under 60 on C the result, 102, on D. The figures in the answer are obvious. When there are more factors to take into account, we place the cursor over 102 on D, bring the next divisor on C to the cursor, move the cursor to the next multiplier on C, bring the next divisor on C to the cursor, and so on, until all the factors have been dealt with. Note that only the first factor and the result are read on D; also _that the cursor is moved for multiplying and the slide for dividing_.