Multiplying Decimals. Multiply $0.65 by 3. $0.65 3 $1.95 Multiply $0.65 by 30. $0.65 30 $19.50 We can see, then, that when we multiply a decimal by a whole number the number of decimal places in the answer must be the same as the number of decimal places in the number to be multiplied. Multiply 55 by .3. 55 .3 16.5 In multiplying a whole number by a decimal, there must be as many decimal places in the answer as in the multiplier. Multiply 0.5 by 0.3. One-tenth of 0.5 is five-hundredths. One-tenth of $0.50, or five-tenths of a dollar, is $0.05, or fivehundredths of a dollar. Three-tenths of $0.50 is 3 times as much as one-tenth of $0.50, so $0.50 X 0.3 = $0.15. So we see that in multiplying a decimal by a decimal there must be as many decimal places in the answer as there are decimal places in both the multiplier and the number multiplied taken together. 2 Dividing Decimals. Decimals are divided exactly as whole numbers are divided. Great mistakes are often made, however, by putting the decimal point in the wrong place. It is necessary to learn the rules for locating the decimal point. 1. If the divisor and the number divided have the same number of decimal figures there are no decimal figures in the answer. Example: Divide $6.25 by $1.25. 1.25) 6.25 (5 answer. 2. If the dividend or number divided has more decimal figures than the divisor, then find how many more decimal figures the dividend has than the divisor and this number will be the number of decimal figures in the answer. Example: If there are three decimal figures in the dividend and one in the divisor there will be two decimal figures in the answer. Divide 30.225 by 1.5. 1.5) 30.225 (20.15 answer. 30 22 15 75 75 3. If a decimal is divided by a whole number the answer will have as many decimal figures as the decimal which is divided. Examples to be solved: 1. Multiply $5.50 by .3.-Answer, $1.650. 4. How much is fifteen-hundredths of $425, that is $425. multiplied by 0.15?—Answer, $63.75. 5. Five per cent of a number is the same as fivehundredths of the number. How much is five per cent of $350?-Answer, $17.50. 6. In the same way find six per cent or six-hundredths of $3,525.-Answer, $211.50. 7. If property is taxed 7 mills on the dollar, what is the tax on property assessed at $2,000? -Answer, $14. 8. If the tax levy is 81⁄2 mills on the dollar, what is the tax on $3,500? Multiply by .0085.- Answer, $29.75. 9. Find five and one-half per cent of $350. Multiply by .055.-Answer, $19.75. 10. Divide 61.5 by 1.5.-Answer, 41. 12. If coal cost $2.25 a ton and $240.75 is paid for coal, how many tons are bought? Answer, 107. – 13. Divide $302.25 by 5.-Answer, $60.45. 14. Divide $302.25 by 6.-Answer, $50.375. 15. How many tons of coal at $1.75 a ton can I buy for $73.00?-Answer, 41 tons. 16. What is the weight in pounds of 6.8 tons of coal?-Answer, 13,600 pounds. 17. At $2.75 a ton what is the cost of 50 tons of coal? Answer, $135.00. Adding and Subtracting Decimals. Rule: To add or subtract decimals, write units of the same order in same column. Then add or subtract, as with whole numbers. The decimal point in the answer will be directly under the decimal point of the numbers. Example: Add $308.25 450.565 250.25 $1009.065 Answer. Subtract 355.25 from 1500.75. $1500.75 355.25 $1145.50 Answer. Examples to be solved. 1. Add $250.55, $340.65, $75.15.-Answer, $666.35. 2. Add $56.25, $105.565, $240.50.-Answer, $402.315. 3. Subtract $85.75 from $125.55.-Answer, $39.80. 4. Subtract $155.655 from $278.70.-Answer, $123.045. 5. Subtract $256.255 from $1075.555.-Answer, $819.30. Use of Decimal Fractions in Finding Circumference and Area of a Circle. The engineer should know how to find the horsepower of a steam engine. In order to do this it is necessary to find the number of square inches in the piston; that is, to find the area of the end of the piston, which is a circle. He should also know how to find the contents of a tank or cistern, and to do this he must first find the area of the bottom of the tank, which is usually a circle. In finding the area of a circle, decimals are used. We have learned how to |