bales, the total value of which is $1,000,000,000 and, including the seed, $1,200,000,000." The figure for the number of bales implies that every single bale of cotton raised in the United States was accounted for and that these figures are absolutely accurate down to one bale of cotton. This denotes an accuracy of 1 part in 16,000,000 parts, or an accuracy within 0.000006 per cent. It is very doubtful indeed whether the figures for the cotton crop are accurate within 1,000 or even 10,000 bales. Suppose a possible error of 10,000 bales were assumed, and the cotton crop put down as 16,250,000 bales, the accuracy would still be 1 in 1,625, or within 0.06 per cent. For most purposes it would be much preferable to use the round number 16,250,000 instead of the detailed figures which were given in the Government report. The particular report from which the figures are taken is not a tabulation, but a written report in regard to the methods used for packing cotton. Since the report was intended to be read by merchants and planters, rather than by statisticians, it is all the more important that the figures should be presented in round numbers so that they may be easily grasped. The mere fact that values for the cotton in the latter part of the quotation given above are in very rough estimates of such round numbers as "$1,000,000,000", calls special attention to the use of detailed figures for the "16,250,276 bales".
Misleading figures implying a greater accuracy than justifiable are very often found as a result of the addition of different quantities some of which are large and some small. The small quantities may have a great degree of accuracy, but this does not give accuracy to the sum of all the quantities, for the total cannot be any more accurate than the most inaccurate item included in the total. 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 slide 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
