If a very large item is not accurate within ten thousand, then it is useless to include in the grand total the three right-hand digits which may be obtained as the result of addition. When some of the items included are so small that they are in tens or hundreds, the addition should be made to include all the digits. After the sum is known then all those digits whose accuracy is doubtful in the total should be replaced by ciphers.

Fictitious accuracy is quite often implied in the results of computations where a shde rule has been used. The ordinary 10-inch slide rule can give an accuracy of only three significant figures, and, on the right-hand portion of the scale, the third figure is often somewhat in doubt unless very great care is used in manipulating the

328 GRAPHIC METHODS

rule. This means that with the 10-inch sHde rule the accuracy is ordinarily no greater than 1 in 1,000, or one-tenth of one per cent. Though two quantities each running into five figures may be multiplied on the slide rule, the product would not be accurate beyond three significant figures, and ciphers must be put down to express the remainder of the number for the product.

If very large quantities obtained by slide-rule computation are added together with a number of small quantities, the total cannot, of course, be accurate beyond the third or fourth digit toward the right of the largest ciuantity included in the total. The fourth digit may be fairly accurate in the total, because in the process of addition the various figures added would tend to give a close approximation of the fourth digit and that digit might accordingly be put down in the total because it has at least a fair possibility of accuracy.