By LearningExpress Editors
Updated on Sep 26, 2011
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.
 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.
 c. Change all of the comparisons to decimals by dividing the number offreethrows 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 freethrow shooter. Addzeros to the ends of the decimals to compare easily. The shooters arelisted from best to worst below.
 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.
50.20
50.24
50.32
50.90
The smallest time is 50.20 seconds.
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
0.810 Charles
0.745 Larry
0.633 Michael
0.546 John
More practice problems on decimals word problems can be found at:
 Decimals Word Problems Practice Questions Set 1
 Decimals Word Problems Practice Questions Set 2 (You are here)
 Decimals Word Problems Practice Questions Set 3
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