Cyphers annexed to decimals, neither increase nor decrease their value; 35000, and 35 are equal; but prefixed, decrease them in a ten-fold proportion; 3, 03, 003 all express different decimals, and are equal to TTOOO. 3 NOTE.-In Decimals 1-4th of any thing is equal to 25, 1-2 equal to ⚫5, and 3-4ths to 75, &c. &c. Addition of Decimals. RULE. Place the numbers so that the points may stand under each other, and then proceed as in Simple Addition. 3. Find the sum of 3.075 + 175 +.1.30 + 6.7 + .6 Anf. 11.850. 4. If 346.784 + 96.9 + 4.321 60.073 .300.003 .013, be added together, what is the sum? Anf. 808.094. Subtraction of Decimals. RULE. Place the numbers, as in Addition, with the least under the greatest, then subtract as in Simple Subtraction, and in the difference observe to set the point directly under those in the example. Examples. From 100.64 take 64.321 and what is left. Anf. 36.319. 5. What is the difference between 3860.75. and .1.1666. Anf. 3859.5834. 6. What is the difference between 16.433. and 9.16? Anf. 7.273 Multiplication of Decimals. RULE. Place the numbers as in Simple Multiplication, and multiply accordingly, remembering to point off as many places for decimals in the product, as there are decimals in both factors: but if decimal places be wanting in the product, supply them with cyphers to the left hand. NOTE.-Multiplication of Decimals may be contracted, by setting the units figure of the multiplier, under such place of the multiplicand as is to be the lowest retained in the product; and placing all the remaining figures of the multiplier in an inverted order: in multiplying begin with the figure in the multiplicand, which stands over the multiplying figure, adding the increase which may arise, by carrying one for the first five, and one more for every ten after, and placing the products so, that the right hand figures stand under each other. Anf 165.6994 6. Multiply 3.141592 by 52.7438, and leave only four pla ces of decimals in the product. 7. Multiply 2.38645 by 8.2175, and reserve only four pla ces of decimals in the product. 8. Multiply 27.14986 by 92.41035, of decimals in the product. 9. Multiply 184.8207 by 13.57493, places of decimals in the product. Anf. 19.6107 and retain six places Anf. 2508.928065 retaining only three Anf. 2508.928 10. Multiply 674.4375 by 27 368, reserving only the inte gers in the product. Anf. 18458. When any number of decimals is to be multiplied by 10, 100, 1000, &c. it is only removing the separating point in the multiplicand so many places towards the right hand, as there are cyphers in the multiplier: thus, .578 X 10:5-78·578 X 100 57.8 .578.X 1000.578. &c. &c. Division of Decimals. RULE. Divide as in Simple Division, pointing off as many figures for decimals, in the quotient, as the dividend has more than the divisor. NOTE 1. If the divisor and dividend have both the same number of decimal parts, the quotient will be a whole number. 2. If the dividend has not so many places of decimals as are in the divisor, then so many cyphers must be annexed to the dividend as will make them equal, and the quotient will then be a whole number. 3. But if when the division is done, the quotient has not so many figures, as it should have places of decimals, then so many cyphers must be prefixt ed as there are places wanting. 2. Divide 3857.60846785 by .384758 fo. Divide .3 by 3. Answer 10026.06 +- Answer .010395 + Answer .1 Answer .1 When numbers are to be divided by 10, 100, 1000, &c. it is performed by placing the feparating point in the dividend fo many places towards the left hand, as there are cyphers in the divisor. Thus, 378410 - 378.4 3784100 37.84 f 3784 1000 3.784 378410000 = 3784 Contracted Division. RULE. -What ever place of the dividend corresponds with the units place of the divifor, at the setting out of the divifion, the fame place muft the first figure of the quotient have. When dividing, reject the laft right hand figure of the divifor, at every step, (inftead of bringing down a figure as is common) and make the laft remainder the dividend for the new divifor at every ftep: thus continuing the divifion until the divisor be exhaufted. 11. Examples. 99.5678)4.6789837568(.0469931 Answer. 597402 99.567)696271 Here, the units place of the divifor in the fetting out of the divifion falls under 7. in the place 99.56)98869 of hundredths in the dividend; 89604 therefore I put 4 the first quoti ent figure in the place of hun99.5)9265 dredths, by prefixing a cypher. 8955 Every divisor is set down to explain the operation ; but you need 99.310 only dafh every figure rejected, 297 as you proceed to fhew it is omitted. 9/13 Remainder 12. Divide 6109.2674 by 240.649 and let there be 4 places of decimals in the quotient. Answer 25.3451+ 13. Divide 913.08 by 2137.2, and leave 3 places of deciAnswer .427 + mals. NOTE. That in working in Contracted Divifion, we come nearer the truth, by multiplying every figure left out in the divifor, when we carry 1. if it be 5 or upwards to 15: if 15 or upwards to 25, 2: If 25, or upwards to 35. 3, &c. The two laft examples above are performed, with observation to this note. Reduction of Decimals. To reduce a Vulgar Fraction to a Decimal. RULE.-Annex as many cyphers to the numerator as may be neceffary, which divide by the denominator, the quotient will be the decimal. Examples 1. Reduce to a decimal 4)1.00 25 Anf |