A Familiar Explanation of the Elementary Rules of Arithmetic. (a Familiar Explanation of the Higher Parts of Arithmetic. 2nd Ed.) - Softcover
Synopsis
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1852 edition. Excerpt: ... ten times less than it would have been, had the 6 been in the units' place; hence I place every figure in this product one place farther to the right than in the previous line; so, also, the product by the 8 will be two places to the right, by the 5, will be three places, &c. Again, since the 9 in the multiplier represents 90, I place the product obtained by multiplying by the 9 one place more to the Icjt than the first product; and if there were any figures in the places for hundreds, thousands, &c. of the multiplier, I should place the corresponding products two, three, &c. places to the left. The whole of the work will now be intelligible. The above row of products may be written down in any order we please; provided that, in commencing the multiplication by any other figure than the one in the units' place, we use proper caution in placing the product in its proper situation with respect to the decimal point. 118. If it be required that the product of two decimals be correct only to a certain number of decimal places, the above work may be contracted. For instance, let it be required to find the product of 7.24651 and 81.4632, correct to 4 places of decimals. First working the Ex. at full length, we have By drawing a vertical line between the 5th and 6th columns, I cut off to the left that part of the product which will furnish the required 4 decimal places. Now it must be observed that the column marked (A) is formed of the following products: viz. 7 in the upper line by 2 in the lower; 2 in the upper by 3 in the lower; 4 in the upper by 6 in the lower; 6 in the upper by 4 in the lower; 5 in the upper by 1 in the lower; 1 in the upper by 8 in the lower: but in forming this column alone, we must allow for the figures...
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