To find the Value of a decimal Fraction, in the known Parts of the Integer. Multiply the decimal proposed into the number of equal parts contained in the integer, and the product will be the number of such parts as are expressed by the fraction. What is the value of .25 of a pound sterling? 20 Answer shillings 5.00 25 For. 25 or 0% of one pound, is equal to the one hundredth part of 25 pounds, or of the shillings in 25 pounds, which are 500; therefore the one hundredth part thereof will be 5 shillings; which is effected by cutting off the two cyphers, for the two decimals by a point. What is the value of .385 of a pound sterling? 20 Shillings 7.700 12 Pence 8.400 4 Farthings 1.600 What is the value of .48 of a chain of 50 links? 50 Answer links 2400 What is the value of .2864 of a shilling? What is the value of .287 of a pound weight troy? Oz. Dwt Gr. Answer 3 8 21 What is the value of .2945 of a pound avoirdupoise? THE EXTRACTION OF THE SQUARE ROOT. A SQUARE number is the product of a number multiplied by itself; and the number so multiplied, is called the root of that square; thus 9 is the square of 3, and 3 is the root of 9, for 3 multiplied by 3 is 9. If a square number be given to find its root, observe if the number of figures or places in the given square be odd or even, if they be odd, find the root of the first figure; but if they be even, of the two first; under which place the square of that root, and deduct, placing the root in the quotient, and bring down two figures to the remainder. Let the double of the said root be made a divisor to all the figures of that last remainder, except the last; put the quotient thereof with the root, or former quotient; and having multiplied it into the numbers so formed, deduct the product from the foregoing figures or resolvend; and in like manner proceed, till all the figures of the given square are exhausted, If there be any decimals in the given square, their number must be even, or made so, before we begin to find the root, by adding a cypher to the right hand; and for every two places of decimals in the square, let one be cut off in the root. EXAMPLES. 1. What is the square root of this square number, 298116? 29,81,16(546 25 104)481 1086).6516 Because the number of figures in the given square number is even, we find the nearest square number to the first two figures 29, which is 25, the root whereof 5, we set in the quotient, and deduct 25 from 29, and to the residue 4, we annex the following figures 81, so we have 481 for a resolvend. The double of the first figure in the quotient being 10, is then set as a divisor to 48, all the figures in the resolvend, but the last; and finding it to be contained 4 times, we anuex the 4 to the divisor and quotient ; the then divisor, 104 is multiplied by the last figure in the quotient, 4, and the product 416 is deducted from the resolvend 481, to the residue whereof is annexed the two following figures in the square, so we have 6516 for a new resolvend, to all which figures but the last we make 108, the double of 54, the figures in the quotient a divisor, and finding it will be contained 6 times, we place 6 in the divisor and quotient; the then divisor 1086 is multiplied by the last figure in the quotient 6, and the product being set under the resolvend and thence deducted, leaves nothing; so is 546 the root sought, For if the root 546 be squared or multiplied by 546, the product will be the square number given. 2. What is the square root of 1710864? Root 1,71,08,64(1308 Answer 1 23).71 69 2608).20864 What is the square root of 3857.3 ? Here being an odd decimal figure, we annex any odd number of cyphers to make the decimal places even; and then extracting the root as before, we thence cut off half the number of decimals that we have in the square. Thus, Root. 3857.300000(62.107 Answer. 36 122)257 1241)1330 1241 124207)890000 |