The word and should be used in reading numbers only between a whole number and a decimal. Exercise 2 Read the following decimals: 1. .2; .02; .002 2. 1.2; 1.02; 1.002 3. 300.7; 8.012; 9.08 4. 0.005; 7.03; 1.03 5. .0005; 92.3; 75.02 6. .7854; 3.1416; 75.02 7. .32605; .000625; 7.9 8. 8.002; .00825; 3.014 9. .625; 60.06; 32.7 10. 1.015; 50.01; 2.0002 11. 100.001; .101; 100.101 12. 5.75; 19.002; 4.0067 13. 90.075; .866; 1.4142 14. 2150.42; 4.065; 3.003 15. 82.03; 92.057; 2.204 16. 2.54; .00125; .003175 Exercise 3 In writing decimals, ask yourself how many places there are in the decimal; then how many figures there are in the number you are to write and prefix the necessary number of zeros before the number to fill in the required number of decimal places. For example: Write seventy-five ten-thousandths. There are four places in the decimal; there are two figures in the number. Therefore, there must be two zeros prefixed to the 75 to fill in the required number of decimal places. Then, seventy-five ten-thousandths =.0075. In some books an extra zero is prefixed before the decimal point as here shown-0.075—in order that the decimal point stands out more clearly. It is omitted in most cases in this book, because it is regarded as unnecessary and requires extra time for writing it. Write these decimals. 1. One one-hundredth. 2. Two hundred five ten-thousandths. 3. Sixty-three thousandths. 4. Twenty-five hundred-thousandths. 5. Seven hundred fifteen thousandths. 6. Eighty-seven thousandths. 7. Nine hundred forty thousandths. 8. Sixty-three hundredths. 9. Sixty-seven thousandths. 10. Eight millionths. 11. Three and one thousand four hundred sixteen tenthousandths. 12. Five thousand two hundred thirty-six ten-thousandths. Exercise 4. Addition of Decimals Decimals are arranged in columns for addition in the same manner that whole numbers are, tenths being placed under tenths, hundredths under hundredths, etc. In what order will the decimal points fall? Example: Add 10.7 and 21.92. 10.7 Arrange these numbers so that the decimal points are in a vertical line. There are no hundredths to add to the 2 21.92 hundredths, so we bring the 2 hundredths down to the 32.62 hundredths place in the sum. What is the sum of 9 tenths and 7 tenths? How many tenths make a whole unit? How many tenths are left out of 16 tenths after making a whole unit? Bring this number of tenths down in tenth's place in the sum. Add the 1 unit to the 1 unit in the units' column, making 2 units, and the 2 tens to the 1 ten, making 3 tens. The sum, then, is 32.62. Add: 1. 2.7 and .3 11. 37.5 and 56.75 2. 37.1 and 2.4 12. 3.12 and 31.2 3. 105.6 and 50.4 13. 104.36 and 2.57 4. 6.67 and .33 14. 28.75 and 71.25 6. 9.99 and 0.01 16. 33.33} and 66.663 6. 75.75 and 24.25 16. 28.48 and 71.12 7. 73.25 and 1.75 17. .99 and .265 8. 999.99 and 0.01 18. .009 and .991 9. 28.8 and 1.27 19. 87.4 and 15.6 10. 1000.01 and 999.09 20. .0045 and 25.0055 21. Mrs. McFarland's light bills for the past six months were: $1.73; $1.68; $2.12; $1.88; $2.03, and $1.85. Find the total sum of her bills for the past six months. 22. Edwin bought the following bill of groceries at a store: sugar, $0.69; bread, $0.15; a can of salmon, $0.28; eggs, $0.32, and potatoes, $0.25. Find the amount of his bill of goods. 23. A Boy Scout fitted up a wireless station at the following cost for materials: 1 pound No. 20 copper wire, $0.46; 12 porcelain cleat insulators, $0.18; 1 pound No. 14 aluminum wire, $0.48; 1 double binding post, $0.12; 10 single binding posts, $1.00; old brass, $0.15; 2 feet 1 inch brass rod, $0.20; tin foil, $0.10, and 1 pair of standard telephone receivers, $5.00. Find the total cost of his materials. 24. How many tons of coal were there in five loads weighing 1.42 tons, 1.382 tons, 1.463 tons, 1.35 tons and 2.481 tons? 25. Helen bought an arithmetic for $0.50, a reader for $0.45, a tablet for $0.05 and a bottle of library paste for $0.05. How much was the sum of her purchases? Y 26. The rainfall at a certain city in a recent year was as follows: January, 2.39 inches; February, 2.76 inches; March, 4.21 inches; April, 5.15 inches; May, 4.27 inches; June, 2.05 inches; July, 2.38 inches; August, 1.09 inches; September, 2.58 inches; October, 3.19 inches; November, 2.80 inches; December, 1.47 inches. What was the total rainfall for the year? Exercise 5. Subtraction of Decimals Decimals are subtracted in the same way that whole numbers are, the decimal points falling in a vertical line; tenths under tenths, hundredths under hundredths, etc. Subtract 3.127 from 4.5. 4.500 Is 4.500 of the same value as 4.5? Since adding zeros to the right 3.127 of a decimal fraction does not change its value, we may fill in the hundredth’s and thousandth’s places in the minuend with zeros 1.373 and subtract by the same method as used in whole numbers. Where do we place the decimal point? Subtract the following: 1. 4.231-1.927 8. 800.75–775.25 16. 36 ft.-6.3 ft. 2. 6.5-3.25 9. 15.06-9.18 16. 43.19-27.17 3. 18.3–9.375 10. 396.09- 247.9 17. 2.125-1.0025 4. 24.85-16.39 11. 36.112–29.802 18. 6.5-3.625 5. 10-7.875 12. $45.25-$29.35 19. $14.85 - $9.50 6. 4-1.003 13. $10-$7.63 20. 716.88-528.4 7. 3.05-1.26 14. $25-19.07 21. 136.97-58.84 22. John had $48.75 in his savings bank account and took out $4.50 to buy some shoes. How much did he have left in his account? 23. Ruth made $12.00 during the vacation. She spent $5.85. How much did she have left,? Every year in different cities of our country there are held athletic contests at which championships in different sports are decided. The ice skating records made at both indoor and outdoor contests in a recent year were as follows: Event U.S. Records Canadian 220 yards 22.4 seconds 440 yards 41.2 seconds 40.2 seconds mile 1.38 minutes 1.45 minutes 1 mile 2.92 minutes 3.106 minutes 24. Find which is the lowest record in each event, and how much-the Canadian or United States records. 25. A quart of milk weighs 2.155 pounds and a quart of water weighs 2.088 pounds. How much heavier is a quart of milk than a quart of water? Exercise 6. Multiplication of Decimals 1. Multiply .25 by .5 Express .25 as a common fraction 10% and .5 as a common fraction B. Then 100X1% - 10% : 100o as a decimal =.125 Then .25 X.5 =.125 1 2 5 1 2 5 How does the number of decimal places in the product (.125) compare with the number of decimal places in both the multiplier (.5) and the multiplicand (.25)? |