Hence, for the addition of decimal numbers, 1. Set down the numbers to be added so that figures occupying places of the same value shall fall directly under each other. II. Then add as in simple numbers and point off in the sum, from the right hand, so many places for decimals as are equal to the greatest number of places in any of the added numbers. EXAMPLES. 1. Add 4.035, 763.196, 445.3741, and 91.3754 together. Ans. 2. Add 365.103113, .76012, 1.34976, .3549, and 61.11 together. Ans. 428.677893. 3. 67.407 +97.004+4+.6+.06+.3=169.371. 4. .0007+1.0436+.4+.05+.047=1.5413. 5. .0049+47.0426 +37.0410+360.0039=444.0924. 6. What is the sum of 27, 14, 49, 126, 999, .469, and .2614? Ans. 1215.7304. 7. Add 15, 100, 67, 1, 5, 33, .467, and 24.6 together. 8. What is the sum of 99, 99, 31, .25, 60.102, .29, and 100.347 ? Ans. 9. Add together .7509, .0074, 69.8408, and .6109. 10. Required the sum of twenty-nine and 3 tenths, four hundred and sixty-five, and two hundred and twentyone thousandths. Ans. 11. Required the sum of two hundred dollars one dime three cents and nine mills, four hundred and forty dollars nine mills, and one dollar one dime and one mill ? Ans. $641.249, or 641 dollars 2 dimes 4 cents 9 mills. 12. What is the sum of one-tenth, one hundredth, and one thousandth ? Ans. 13. What is the sum of 4, and 6 ten-thousandths ? Ans. 4.0006. 14. Required in dollars and decimals, the sum of one dollar one dime one cent one mill, six dollars three mills, four dollars eight cents, nine dollars six mills, one hundred dollars six dimes, nine dimes one mill, and eight dollars six cents. Ans. 1. get for all ? 15. What is the sum of 4 dollars 6 cents, 9 dollars 3 mills, 14 dollars 3 dimes 9 cents 1 mill, 104 dollars 9 dimes 9 cents 9 mills, 999 dollars 9 dimes 1 mill, 4 mills, 6 mills, and 1 mill ? Ans. $1132,365. 16. If you sell one piece of cloth for $4,25, another for $5,075, and another for $7,0025, how much do you Ans. $16,3275. 17. What is the amount of $151,7, $70,602, $4,06, and $807,2659 ? Ans. $1033,6279. 18. A man received at one time $13,25; at another $8,4; at another $23,051; at another $6; and at an. other $0,75 : how much did he receive in all ? Ans. $51,451. 19. Find the sum of twenty-five hundredths, three hundred and sixty-five thousandths, six tenths, and nine millionths. Ans. 20. What is the sum of twenty-three millions and ten, one thousand, four hundred thousandths, twenty-seven, and nineteen millionths, seven, and five tenths ? Ans. 23001044.500059. 21. What is the sum of six millionths, four ten-thou. sandths, 19 hundred thousandths, sixteen hundredths, and four tenths ? Ans. SUBTRACTION OF DECIMAL FRACTIONS. 168. Subtraction of Decimal Fractions is the process of finding the difference between two decimal numbers. Let it be required from 3.275 to take .0879. In this example a cipher is annexed to OPERATION. the minuend to make the number of de 3.2750 cimal places equal to the number in the .0879 subtrahend. This does not alter the 3.1871 value of the minuend (Art. 122). Hence, for the subtraction of decimal numbers, ? How many 168. What does subtraction teach? How do you set down the numbers for subtraction? How do you then subtra decimal places do you point off in the remainder ? I. Set down the less number under the greater; so that figures occupying places of the same value shall fall di. rectly under each other. II. Then subtract as in simple numbers, and point of in the remainder, from the right hand, as many places for decimals as are equal to the greatest number of places in either of the given numbers. EXAMPLES. 1. From 3295 take .0879. Ans. 3294.9121. 2. From 291.10001 take 41.375. Ans. 249.72501. 3. From 10.000001 take .111111. Ans. 9.888890. 4. From three hundred and ninety-six, take 8 ten. thousandths. Ans. 5. From 1 take one thousandth. Ans. .999. 6. From 6378 take one tenth. Ans. 6377.9. 7. From 365.0075 take mill aths. Ans. 365.007497. 8. From 21.004 take 97 ten-thousandths, Ans. 9. From 260.4709 take 47 ten-millionths. Ans. 260.4708953. 10. From 10.0302 take 19 millionths. Ans. 10.030181. 11. From 2.01 take 6 ten-thousandths. Ans. 12. From thirty-five thousands, take thirty-five thousandths. Ans. 34999.965. 13. What is the difference between 4262.0246 and 23.41653 ? Ans. 14. From 346.523120 take 219.691245943. Ans. 126.831874057. 15. From 64.075 take .195326. Ans. 16. What is the difference between 107 and .0007? Ans. 106.9993. 17. What is the difference between 1.5 and .3785 ? 18. From 96.71 take 96.709. Ans. .001. 19. From forty-three, and seventy-five thousandths, take eight, and twenty-three millionths. Ans. MULTIPLICATION OF DECIMAL FRACTIONS. 37 8 OPERATION. 37 .37=107 296 169.–1. Multiply .37 by .8. We may first write .37=ido, and .8=16 If, now, we multiply the fraction 10% by , we find the product to be 00%; the number of ciphers in the denominator of this product is equal to the number of decimal places in the two factors, and the same will be true for any two factors whatever. 2. Multiply .3 by .02. .8= .296=1000 296 =.296. OPERATION. 02 .3x.02=lo X1%%=10%=.006 answer. Now, to express the 6 thousandths decimally, we have to prefix two ciphers to the 6, and this makes as many decimal places in the product as there are in both multiplicand and multiplier. Therefore, to multiply one decimal by another, Multiply as in simple numbers, and point off in the product, from the right hand, as many figures for decimals as are equal to the number of decimal places in the multiplicand and multiplier ; and if there be not so many in the product, supply the deficiency by prefixing ciphers. EXAMPLES. 1. Multiply 3.049 by .012. Ans. .036588. (2.) (3.) Multiply 496.0135 by 1.496 Ans. 742.0361960 4. Multiply one and one millionth by one thousandth. Ans. .001000001. 169. After multiplying, how many decimal places will you point off in the product? When there are not so many in the product, what do you do? Give the rule for the multiplication of decimals. 5. Multiply one hundred and forty-seven millionths by one millionth. Ans. 6. Multiply three hundred, and twenty-seven hun. dredths by 31. Ans. 9308.37. 7. Multiply 31.00467 by 10.03962. Ans. 311.2751050254. 8. What is the product of five-tenths by five-tenths ? 9. What is the product of five-tenths by five-thou. sandths ? Ans. .0025. 10. Multiply 596.04 by 0.00004. Ans. 11. Multiply 38049.079 by Ò.00008. Ans. 3.04392632. 12. What will 6.29 weeks' board come to at 2,75 dollars per week ? Ans. $17,2975. 13. What will 61 pounds of sugar come to at $0,234 per pound ? Ans. 14. If 12.836 dollars are paid for one barrel of flour, what will .354 barrels cost? Ans. $4,543944. 15. What is the content of a board, .06 feet long and .06 wide ? Ans. 16. Multiply 49000 by .0049. Ans. 240.1. 17. Bought .1234 oranges for 4.6 cents apiece: how much did they cost ? Ans. 18. What will 375.6 pounds of coffee cost at .125 dol. lars per pound? Ans. $46,95. 19. If I buy 36.251 pounds of indigo at $0,029 per pound, what will it come to ? Ans. $1,051279. 20. Multiply $89,3421001 by .0000028. Ans. $0,00025015788028. 21. Multiply $341,45 by .007. Ans. 22. What is the content of a lot which is .004 miles long and .004 miles wide ? Ans. .000016 sq. miles, 23. Multiply .007853 by .035. Ans. 24. What is the product of $26,000375 multiplied by .00007 ? Ans. $0,00182002625. 170. When a decimal number is to be multiplied by 10, 100, 1000, &c., the multiplication may be made by removing the decimal point as many places to the right hand as there are ciphers in the multiplier, and if there 2 |