_Estimation of the Figures in a Product._—We have given rules for those who prefer to decide the number of figures by this means, but experience will show that to make the best use of the instrument, the result, as read on the rule, should be regarded merely as the _significant figures of the answer_, the position of the decimal point, if not obvious, being decided by a very rough mental calculation. In very many instances, the magnitude of the result will be evident from the conditions of the problem—_e.g._, whether the answer should be 0·3 in., 3 in., or 30 in.; or 10 tons, 0·1 ton, 100 tons, etc. In those cases where the magnitude of the answer cannot be estimated, and the factors contain many figures, or have a number of 0’s following the decimal point, the use of notation by powers of 10 (page 8) is of considerable assistance; but more usually it will be found, that a very rough calculation will settle the point with comparatively little trouble. Considerable practice is needed to work rapidly and with certainty, when using rules. Moreover, the experience thus acquired is confined to slide-rule work. The same time spent in practising the “rough approximation” method will enable reliable results to be obtained rapidly, with the advantage that the method is applicable to calculations generally. However, the choice of methods is a matter of personal preference. Both methods will be given, but whichever plan is followed, the student is strongly advised to cultivate the habit of forming an idea of the magnitude of the result. EX.—33·6 × 236 = 7930. Setting 1 on C to 33·6 on D, we read under 236 on D and find 793 on D, as the significant figures of the answer. A rough calculation, as 30 × 200 = 6000, indicates that the result will consist of 4 figures, and is therefore to be read as 7930. EX.—17,300 × 3780 = 65,400,000. By factorising with powers of 10 1·73 × 10^4 × 3·78 × 10^3 = 1·73 × 3·78 × 10^7. Setting 1 on C to 1·73 on D, we read, under 3·78 on C, the result of the simple multiplication, as 6·54. Multiplying by 10^7 moves the decimal point 7 places to the right, and the answer is 65,400,000. If it is required to find a series of products of which one of the factors is _constant_, set 1 on C to the constant factor on D and read the several products on D, under the respective variable factors. If the factors are required which will give a constant _product_ (really a case of division), set the cursor to the constant product on D. Then obviously, as the slide is moved along, any pair of factors found simultaneously under the cursor line on C, and on D under index of C, will give the product. A better method of working will be explained when we deal with the inversion of the slide.