Decimals Word Problems
We use decimals every day–to express amounts of money, or to measure distances and quantities. This set of practice problems includes word problems that help you practice your skills in rounding decimals, as well as performing basic mathematical operations with them.
- Find the product of 5.2 × 10^{3} and 6.5 × 10^{7}. Write your answer in scientific notation.
- 33.8 × 10^{21}
- 3.38 × 10^{11}
- 33.8 × 10^{10}
- 3.38 × 10^{9}
- Brian's 100-yard dash time was 2.68 seconds more than the school record. Brian's time was 13.4 seconds. What is the school record?
- 10.72 seconds
- 11.28 seconds
- 10.78 seconds
- 16.08 seconds
- Ryan's gym membership costs him $390 per year. He pays this in twelve equal installments a year. How much is each installment?
- 1170
- 42.25
- 4680
- 32.5
- How much greater is 0.0543 than 0.002?
- 0.0343
- 0.0072
- 0.0523
- 0.0563
- Kevin ran 6.8 miles yesterday and 10.5 miles today. How many more miles did he run today?
- 3.7
- 4.7
- 4.3
- 5.9
- Jay bought twenty-five $0.39 stamps. How much did he spend?
- 5.69
- 7.84
- 2.88
- 9.75
- Which number falls between 5.56 and 5.81?
- 5.54
- 5.87
- 5.6
- 5.27
- Hanna's sales goal for the week is $5,000. So far she has sold $3,574.38 worth of merchandise. How much more does she need to sell to meet her goal?
- 2425.38
- 1329.4
- 2574.38
- 1425.62
- Which of the following decimals is the greatest number?
- 0.064
- 0.007
- 0.1
- 0.04236
- Andy earned the following grades on his four math quizzes: 97, 78, 84, and 86. What is the average of his four quiz grades?
- 82.5
- 86.25
- 81.5
- 87
- Luis runs at a rate of 11.7 feet per second. How far does he run in 5 seconds?
- 585 feet
- 490.65 feet
- 58.5 feet
- 55.5 feet
- Nancy, Jennifer, Alex, and Joy ran a race. Nancy's time was 50.24 seconds, Jennifer's was 50.32, Alex's was 50.9, and Joy's was 50.2. Whose time was the fastest?
- Nancy
- Jennifer
- Alex
- Joy
- Mike can jog 6.5 miles per hour. At this rate, how many miles will he jog in 1 hour and 30 minutes?
- 9.75 miles
- 4.7 miles
- 9 miles
- 10.75 miles
- What decimal is represented by point A on the number line?
- 0.77
- 0.752
- 0.765
- 0.73
- Nicole is making 20 gift baskets. She has 15 pounds of chocolates to distribute equally among the baskets. If each basket gets the same amountof chocolates, how many pounds should Nicole put in each basket?
- 1.3 pounds
- 0.8 pounds
- 0.75 pounds
- 3 pounds
- A librarian is returning library books to the shelf. She uses the call numbers to determine where the books belong. She needs to place a book about perennials with a call number of 635.93. Between which two call numbers should she place the book?
- 635.8 and 635.9
- 635.8 and 635.95
- 635.935 and 635.94
- 635.99 and 636.0
- Michael made 19 out of 30 free-throws this basketball season. Larry's free-throw average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-throw shooter?
- Michael
- Larry
- Charles
- John
- Which number below is described by the following statements? The hundredths digit is 4 and the tenths digit is twice the thousandths digit.
- 0.643
- 0.0844
- 0.446
- 0.0142
- If a telephone pole weighs 11.5 pounds per foot, how much does a 32-foot pole weigh?
- 368 pounds
- 357 pounds
- 346 pounds
- 338.5 pounds
- Amy purchased 6 books at $4.89 each. How much did the books cost altogether?
- 24.84
- 25.56
- 29.34
- 30.14
Answers
- b. To multiply numbers written in scientific notation, multiply the first numbers (5.2 × 6.5 = 33.8). Then, multiply the powers of ten by adding the exponents (10^{3} × 10^{7} = 10^{10}); 33.8 × 1010 is the answer, except it is not in scientific notation. The decimal in 33.8 must be moved to create a number between 1 and 10. Placing the decimal between the 3s will accomplish this (3.38). Since the decimal has been moved once to the left, the exponent of ten must be increased by 1. The answer is 3.38 × 10^{11}.
- a. The school record is less than Brian's time. Therefore, 2.68 must be subtracted from 13.4; 13.4 – 2.68 = 10.72. To subtract decimals, line up the numbers vertically so that the decimal points are aligned. Since 13.4 has one less decimal place than 2.68, you must add a zero after the 4 (13.40) before subtracting. After you have done this, subtract normally. If you chose d, you added instead of subtracted.
- d. To find each installment, the total yearly cost ($390) must be divided by the number of payments (12); 390 ÷ 12 = $32.50. Choices a and c do not make sense because they would mean that each monthly installment (payment) is more than the total yearly cost.
- c. To find out how much greater a number is, you need to subtract; 0.0543 – 0.002 = 0.0523. To subtract decimals, line the numbers up vertically so that the decimal points align. Then, subtract normally. If you chose a, you did not line up the decimal places correctly. The 2 should go under the 4. If you chose d, you added instead of subtracted.
- a. To find out how many more miles he ran today, subtract yesterday's miles from today's miles; 10.5 – 6.8. To subtract decimals, line the numbers up vertically so that the decimal points align. Then, subtract normally. If you chose b, you made an error in borrowing. You forgot to change the 10 to a 9 when borrowing 1 for the 5.
- d. To find how much Jay spent, you must multiply the cost of each stamp ($0.39) by the number of stamps purchased (25); $0.39 × 25 = $9.75. To multiply decimals, multiply normally, then count the number of decimal places in the problem. Place the decimal point in the answer so that it contains the same number of decimal places as the problem does.
- c. If you add a zero to the end of 5.6 to get 5.60, it is easier to see that 5.56 < 5.60 < 5.81. choice a is less than 5.56. choice b is greater than 5.81. choice d is less than 5.56.
- d. You must find the difference (subtraction) between her goal and what she has already sold. Add a decimal and two zeros to the end of $5,000 ($5,000.00) to make the subtraction easier; $5,000.00 – $3,574.38 = $1,425.62.
- c. If you add zeros to the end of each of the numbers so that each number has 5 places after the decimal point, it is easier to compare the numbers; 0.00700 < 0.04236 < 0.06400 < 0.10000.
- b. To find the average, you must add the items (97 + 78 + 84 + 86 = 345) and divide the sum by the total number of items (4); 345 ÷ 4 = 86.25. Remember to add a decimal point and zeros after the decimal when dividing (345.00 ÷ 4).
- c. You must multiply 11.7 by 5; 11.7 × 5 = 58.5. To multiply decimals, multiply normally, then count the total number of decimal places in the problem and move the decimal point in the answer so that it contains the same number of decimal places. If you chose a, you forgot to add the decimal point after you multiplied. If you chose d, you forgot to carry a 3 after multiplying 7 by 5 (35, place the 5 below and carry the 3).
- d. The fastest time is the smallest time. To easily compare decimals, add a zero to the end of 50.9 and 50.2 so that they read 50.90 and 50.20. Then compare the four numbers. The times are listed from smallest to largest time below.
50.20
50.24
50.32
50.90
The smallest time is 50.20 seconds.
- a. One hour and thirty minutes is 1 hours or hours. Therefore, multiply the number of miles Mike can jog in one hour by to find the number he can jog in an hour and a half; 6.5 = 9.75 miles.
- a. The hash marks indicate units of 0.01 between 0.75 and 0.80. Point A is 0.77. See the figure below.
- c. Nicole has 15 pounds to divide into 20 baskets. Divide 15 by 20; 15 ÷ 20 = 0.75 pounds per basket.
- b. Quickly compare decimals by adding zeros to the end of a decimal so that all numbers being compared have the same number of decimal places.
choice a does not work:
635.80
635.90
635.93—the book's call number
choice b does work:
635.80
635.93—the book's call number
635.95
choice c does not work:
635.93—the book's call number
635.935
635.94
choice d does not work:
635.93—the book's call number
635.99
636.0
- c. Change all of the comparisons to decimals by dividing the number offree-throws made by the number attempted. Michael's average is 19 ÷30 = 0.633, John's is 0.546, Larry's was given as 0.745, and Charles' wasgiven as 0.81. The largest decimal is the best free-throw shooter. Addzeros to the ends of the decimals to compare easily. The shooters arelisted from best to worst below.
0.810 Charles
0.745 Larry
0.633 Michael
0.546 John
- a. From left to right, the first decimal place is the tenths, the second is the hundredths, and the third is the thousandths. The first criterion is that the hundredths digit is 4. The second decimal place is 4, only in choice a and choice c. The second criterion is that the first decimal place is twice the third decimal place. This is only true in choice a , in which 6 is twice 3.
- a. Multiply 11.5 by 32; 11.5 × 32 = 368 pounds.
- c. Multiply 6 by $4.89; 6 × $4.89 = $29.34.
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