PMI 5 th Grade, Unit 1 Decimal Concepts Chapter Problems Place Value Classwork 1) Write the decimal represented by the shaded portion of the picture on the line (the large square equals one unit). 2) Using the number 6,789,543.0128 what digit is in the: a. Hundreds place? b. Tenths place? c. Millions place? d. Hundred thousands place? e. Thousandths place? f. Ones place? g. Hundredths place? 3) Using the number 67,980,312.9641 what digit is in the: a. Hundred thousands place? b. Thousandths place? c. Tens place? d. Hundreds place? e. Tenths place? f. Hundredths place? g. Millions place? NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org
Homework 4) Write the decimal represented by the shaded portion of the picture on the line (the large square equals one unit). 5) Using the number 647,874.3459 what digit is in the: a. Hundreds place? b. Tenths place? c. Millions place? d. Hundred thousands place? e. Thousandths place? f. Ones place? g. Hundredths place? 6) Using the number 164,987.4907 what digit is in the: a. Hundred thousands place? b. Thousandths place? c. Tens place? d. Hundreds place? e. Tenths place? f. Hundredths place? g. Ones place? Decimals on the Number Line Classwork 7) Label the following numbers on the number line: 0.5, 0.3, 0.9, 0.2 NJ Center for Teaching and Learning ~ 2 ~ www.njctl.org
8) Label the following numbers on the number line: 0.4, 0.1, 0.7, 0.8 9) Label the following numbers on the number line: 0.5, 0.25, 0.75 10) Label the following numbers on the number line: 0.85, 0.35, 0.55, 0.1 Homework 11) Label the following numbers on the number line: 3.5, 3.85, 3.2, 3.35 12) Label the following numbers on the number line: 10.25, 10.75, 10.5 13) Label the following numbers on the number line: 7.1, 7.7, 7.45, 7.3 14) Label the following numbers on the number line: 0, 1, 0.4, 0.65, 0.1, 0.2 NJ Center for Teaching and Learning ~ 3 ~ www.njctl.org
Classwork 15) Write the following numbers in word form. a. 4,325.24 b. 42.976 c. 567.13 d. 0.654 e. 15.006 f. 85,654.37 g. 5.009 h. 6,543,500.81 i. 0.07 j. 632.005 16) Write the following numbers in standard form. a. Sixteen and 73 hundredths b. Nine hundred thirty-three and seven tenths c. Two thousand, five hundred three and twenty hundredths d. Seventy-three thousandths NJ Center for Teaching and Learning ~ 4 ~ www.njctl.org
e. Nine hundred fifteen and sixty-five thousandths f. Eight tenths g. Forty-five thousand, six and seventy-seven hundredths h. Nine hundred fifteen thousandths i. Four hundred five and eighty-nine hundredths j. Seven thousandths Homework 17) Write the following numbers in word form. a. 423.05 b. 9,865.541 c. 64.506 d. 7,854,900.8 e. 0.75 f. 4,000.65 g. 54,612.006 h. 84.156 i. 900.98 j. 0.004 NJ Center for Teaching and Learning ~ 5 ~ www.njctl.org
18) Write the following numbers in standard form. a. Three hundred fifteen and seven tenths b. Nine thousand, six hundred five and seventy-three hundredths c. Seven thousand, and seven thousandths d. Four thousand, seven hundred thirty and three thousandths e. Eight and three hundred twenty-three thousandths f. Six hundred fifty-one and four tenths g. Thirteen thousandths h. Forty-five and ninety-nine hundredths i. Fourteen hundredths j. Six thousand, five hundred forty-three and twenty-one hundredths Comparing with Symbols Classwork 19) Put the correct symbol between each pair of numbers: >, <, = a. 0.45 0.54 f. 0.671 0.618 b. 0.43 0.430 g. 0.042 0.004 c. 0.241 0.251 h. 13.05 13.5 d. 4.23 0.423 i. 8.23 82.3 e. 0.32 0.302 j. 0.479 0.439 NJ Center for Teaching and Learning ~ 6 ~ www.njctl.org
Homework 20) Put the correct symbol between each pair of numbers: >, <, = a. 0.39 0.31 f. 0.9 0.901 b. 0.73 0.073 g. 18.04 18.4 c. 3.5 3.05 h. 0.043 0.05 d. 6.2 6.200 i. 3.2 4 e. 0.712 0.721 j. 0.643 0.609 Ordering Decimals Classwork 21) Use the digits to create the smallest number you can that will be between 0 and 1. a. 4,0,3 b. 5,9,2 c. 3,7,0 22) For each set of numbers, circle the number with the least value and underline the number with the greatest value. a. 11.9702 11.9720 11.9270 11.2907 b. 257.23 275.32 257.32 274.43 c. 0.375 0.85 0.42 0.402 d. 0.007 0.2 0.22 0.3 e. 2.2232 2.3222 2.2223 2.2322 NJ Center for Teaching and Learning ~ 7 ~ www.njctl.org
23) Order the numbers least to greatest a. 0.45, 0.405, 0.04, 0.5 b. 3.7,3.2, 3.09, 3.062, 24) Order the numbers greatest to least. a. 0.81, 0.0008, 81, 0.081, b. 9.3,9.01, 9.32, 9.327, Homework 25) Use the digits to create the largest number you can that will be between 0 and 1. a. 6, 2, 7 b. 0, 6, 1 c. 8, 0, 4 26) For each set of numbers, circle the number with the least value and underline the number with the greatest value. a. 0.2221 0.1121 0.2122 0.1112 b. 3453.2 3342.1 3453.7 3324.9 c. 0.856 0.865 0.685 0.658 d. 0.1 0.101 0.011 0.1011 e. 67.21 76.012 67.012 67.201 NJ Center for Teaching and Learning ~ 8 ~ www.njctl.org
27) Order the numbers least to greatest a. 9.03, 9.008, 9.41, 9.3 b. 0.47, 0.56, 0.6, 0.401 28) Order the numbers greatest to least. a. 7.54, 7.59, 7.03, 7.037 b. 0.007, 0.07, 7, 0.7 Round Numbers to Designated Place Value Classwork 29) What is an advantage and a disadvantage of rounding numbers? 30) Round each of the following to the nearest tenth: a. 43.877 b. 0.796 c. 631.083 d. 5.961 e. 4.712 NJ Center for Teaching and Learning ~ 9 ~ www.njctl.org
31) Round each of the following to the nearest thousandth: a. 52.8097 b. 3.9823 c. 54.0062 d. 6.0499 e. 0.653163 32) Round the following prices to the nearest dollar. Estimate the total cost of all the items? a. $13.75, $2.31, $5.99 b. $0.99, $3.15, $2.89 c. $1.79, $4.09, $3.99 33) Round the following prices to the nearest half-dollar. Estimate the total cost of all the items? a. $5.55, $3.10, $6.89 b. $0.80, $1.20, $1.99 c. $14.45, $10.10, $19.99 NJ Center for Teaching and Learning ~ 10 ~ www.njctl.org
Homework 34) Explain two real life situations where rounding numbers would be helpful. 35) Round each of the following to the nearest hundredth: a. 43.877 b. 0.796 c. 631.083 d. 5.961 e. 4.712 36) Round each of the following to the nearest whole number (one): a. 52.8097 b. 3.9823 NJ Center for Teaching and Learning ~ 11 ~ www.njctl.org
c. 54.0062 d. 6.0499 e. 0.653163 37) Round the following prices to the nearest dollar. Estimate the total cost of all the items? a. $6.99, $4.25, $8.79 b. $0.81, $3.19, $2.80 c. $25.61, $20.40, $23.99 38) Round the following prices to the nearest half-dollar. Estimate the total cost of all the items? a. $15.45, $13.80, $16.99 b. $0.99, $2.22, $7.77 c. $6.80, $3.21, $5.01 NJ Center for Teaching and Learning ~ 12 ~ www.njctl.org
Unit Review Decimal Concepts Multiple Choice Questions 39) Which number represents sixty-nine thousandths? a. 69,000 b. 0.69 c. 0.069 d. 0.0069 40) Which number represents twenty-three and 15 hundredths? a. 23.15 b. 2,315 c. 23.015 d. 150.23 41) Which number represents five hundred fifty-two and two tenths? a. 5,522 b. 552.2 c. 52.2 d. 552.02 42) The number 90.78 is: a. nine and seventy-eight hundredths b. ninety and seventy-eight hundreds c. ninety and seventy-eight thousandths d. ninety and seventy-eight hundredths 43) The number 0.639 is: a. six hundred and thirty-nine hundredths b. six hundred and thirty-nine c. six hundred thirty-nine thousandths d. six hundred thirty-nine thousand 44) The number 7.008 is: a. seventy-eight thousandths b. seven and eight hundredths c. seven and eight thousandths d. seven and eight tenths NJ Center for Teaching and Learning ~ 13 ~ www.njctl.org
45) Which digit is in the tenths place in the number 789.234? a. 2 b. 3 c. 4 d. 8 46) Which digit is in the thousandths place in the number 0.9384? a. 8 b. 4 c. 0 d. 3 47) Which digit is in the ones place in the number 529.673? a. 9 b. 6 c. 7 d. 2 48) Which digit is in the hundredths place in the number 123.4567? a. 4 b. 5 c. 1 d. 6 49) 0.345 0.543 a. > b. < c. = 50) 0.98 0.980 a. > b. < c. = 51) 1.09 0.09 a. > b. < c. = 52) 0.729 0.0729 a. > b. < c. = NJ Center for Teaching and Learning ~ 14 ~ www.njctl.org
53) 0.006 0.016 a. > b. < c. = 54) Which number is the greatest? a. 0.9998 b. 9.998 c. 98.88 d. 9.899 55) Which number is the greatest? a. 0.124 b. 0.0012 c. 0.0421 d. 0.142 56) Which number is the least? a. 3.7 b. 7.3 c. 7.03 d. 0.73 57) Which number is the least? a. 0.1 b. 0.008 c. 0.08 d. 0.02 58) A shirt at the mall is $9.44, a pair of pants is $22.67, and a necklace is $4.25. If you round the cost of each to the nearest dollar, and buy one of each item, what would your estimated total cost be? a. $36.00 b. $35.00 c. $36.50 d. $37.00 NJ Center for Teaching and Learning ~ 15 ~ www.njctl.org
59) At the toy store, a Furby costs $57.78, a teddybear costs $12.32, and a skateboard costs $20.51. If you buy one Furby, two teddybears and one skateboard, what would your estimated total cost to the nearest dollar be? a. $101 b. $91 c. $102 d. $103 60) Joanna sells ice cream cones for $1.99, brownies for $0.56, and cookies for $1.20. If William rounds the cost of each to the nearest half dollar, and wants one of each dessert item, what would his estimated cost be? a. $4.50 b. $3.00 c. $3.80 d. $4.00 Decimal Concepts Short Constructed Response Questions 61) Write the decimal represented by the shaded portion of the picture on the line. (The large square equals one unit.) 62) Write 432.08 out with words. 63) Write out 9.064 with words. 64) What is three hundred and seven hundred thirty-one thousandths in numbers? NJ Center for Teaching and Learning ~ 16 ~ www.njctl.org
65) What is nine and nine tenths in numbers? 66) Order the numbers from least to greatest: 8, 8.3, 9, 8.65, 8.9 67) Order the numbers from least to greatest: 0.8, 0.82, 0.809, 0.827 68) Order the numbers from greatest to least: 0.6, 6.0, 0.006, 0.05 69) Use the digits 5, 3, and 1 to create the smallest number you can between 0 and 1. 70) Use the digits 0,1 and 9 to create the largest number you can between 0 and 1. 71) Round 78.701 to the nearest tenth. 72) Round 0.809 to the nearest hundredth. 73) Round 99.91 to the nearest one. 74) Round 78.701 to the nearest hundredth. 75) Round 1.009 to the nearest tenth. NJ Center for Teaching and Learning ~ 17 ~ www.njctl.org
Decimal Concepts Extended Constructed Response Questions 76) a. Label the following numbers on the number line: 6, 7, 6.55, 6.2, 6.8 b. Which number is least? c. Use three of the above numbers to fill in the blanks. < < 77) a. Write the words eight hundred two and eight hundred two thousandths in numbers. b. Round that same number to the nearest tenth and write that number in word form. c. Round that new number to the nearest one. NJ Center for Teaching and Learning ~ 18 ~ www.njctl.org
78) Shaqwana goes to the store for flowers. Roses cost $3.89, Lilies cost $2.40, and Carnations cost $0.72. a. If Shaqwana wants to buy three Roses, two Lilies, and one Carnation, what would her estimated total cost be if she rounded to the nearest dollar? b. What would her estimated cost be if she rounded to the nearest half dollar? c. Would Shaqwana be paying more, less, or the same if she changed her rounding from the dollar to the half dollar? Explain why. NJ Center for Teaching and Learning ~ 19 ~ www.njctl.org
1. 0.16; 0.40; 0.73; 0.50 2. a. 5 b. 0 c. 6 d. 7 e. 2 f. 3 g. 1 3. a. 9 b. 4 c. 1 d. 3 e. 9 f. 6 g. 7 CW-HW Answer Key 4. 0.82; 0.57; 0.80; 0.12 5. a. 8 b. 3 c. nothing d. 6 e. 5 f. 4 g. 4 6. a. 1 b.0 c. 8 d. 9 e. 4 f. 9 g. 7 7. 0.2 0.3 0.5 0.9 8. 0.1 0.4 0.7 0.8 9. 0.25 0.5.75 10. 0.1 0.35 0.55 0.85 11. 3.2 3.35 3.5 3.85 NJ Center for Teaching and Learning ~ 20 ~ www.njctl.org
12. 10.25 10.5 10.75 13. 7.1 7.3 7.45 7.7 7 8 14. 0 0.1 0.2 0.4 0.65 1 15. a. four thousand, three hundred twenty-five and twenty-four hundredths b. forty-two and nine hundred seventy-six thousandths c. five hundred sixty-seven and thirteen hundredths d. six hundred fifty four thousandths e. fifteen and six thousandths f. eighty-five thousand, six hundred fifty-four and thirty-seven hundredths g. five and nine thousandths h. six million, five hundred forty-three thousand, five hundred and eighty-one hundredths i. seven hundredths j. six hundred thirty-two and five thousandths 16.a. 16.73 b. 933.7 c. 2,503.20 d. 0.073 e. 915.065 f. 0.8 g. 45,006.77 h. 0.915 i. 405.89 j. 0.007 17.a. four hundred twenty-three and five hundredths b. nine thousand, eight hundred sixty-five and five hundred forty-one thousandths c. sixty-four and five hundred six thousandths d. seven million, eight hundred fifty-four thousand, nine hundred and eight tenths e. seventy-five hundredths f. four thousand, and sixty-five hundredths g. fifty-four thousand, six hundred twelve and six thousandths h. eighty-four and one hundred fifty-six thousandths i. nine hundred and ninety-eight hundredths j. four thousandths 18.a. 315.7 b. 9,605.73 NJ Center for Teaching and Learning ~ 21 ~ www.njctl.org
c. 7,000.007 d. 4,730.003 e. 8.323 f. 651.4 g. 0.013 h. 45.99 i. 0.14 j. 6,543.21 19.a. < b. = c. < d. > e. > f. > g. > h. < i. < j. > 21.a. 0.034 b. 0.259 c. 0.037 22. a. circle=11.2907; underline=11.9720 b. circle= 257.23; underline= 275.32 c. circle= 0.375; underline= 0.85 d. circle= 0.007 underline= 0.3 e. circle= 2.2223 underline= 2.3222 23.a. 0.04 < 0.405 < 0.45 < 0.5 b. 3.062 < 3.09 < 3.2 < 3.7 24.a. 81 > 0.81 > 0.081 > 0.0008 b. 9.327 > 9.32 > 9.3 >9.01 25. a. 0.762 b. 0.610 c. 0.840 26. a. circle= 0.1112 underline= 0.2221 b. circle= 3324.9 underline= 3453.7 c. circle= 0.658 underline= 0.865 d. circle= 0.011 underline= 0.1011 e. circle= 67.012 underline=76.012 27. a. 9.008 < 9.03 < 9.3 < 9.41 b. 0.401 < 0.47 < 0.56 < 0.6 28. a. 7.59 > 7.54 > 7.037 > 7.03 b. 7 > 0.7 > 0.07 > 0.007 20. a. > b. > c. > d. = e. < f. < g. < h. < i. < j. > 29. Rounding is used to make numbers easier to work with, but results are not precise. 30. a. 43.9 b. 0.8 c. 631.1 d. 6.0 e. 4.7 31. a. 52.810 b. 3.982 c. 54.006 d. 6.050 NJ Center for Teaching and Learning ~ 22 ~ www.njctl.org
e. 0.653 32. a. $22.00 b. $7.00 c. $10.00 33. a. $15.50 b. $4.00 c. $44.60 34. answers will vary 35. a. 43.88 b. 0.80 c. 631.08 d. 5.96 e. 4.71 36. a. 53 b. 4 c. 54 d. 6 e. 1 37. a. $20.00 b. $7.00 c. $70.00 38. a. $46.30 b. $11.00 c. $15.00 Unit Review 39. c 40. a 41. b 42. d 43. c 44. c 45. a 46. a 47. a 48. b 49. b 50. c 51. a 52. a 53. b 54. c 55. d 56. d 57. b 58. a 59. b 60. c 61. 1.0; 4.4;.49 62. four hundred thirty- two and eight hundredths 63. nine and sixty-four thousandths 64. 300.731 68. 6.0 > 0.6 > 0.05 > 65. 9.9 0.006 66. 8 < 8.3 < 8.65 < 8.9 69. 0.135 < 9 70. 0.910 67. 0.8 < 0.809 < 0.82 < 71. 78.7 0.827 72. 0.81 73. 100 74. 78.70 75. 1.0 76. a. 6 6.2 6.55 6.8 7 b. 6 c. answers will vary 77. a. 802.802 b. eight hundred two and eight tenths c. 803 78. a. $17.00 b. $17.50 c. more; Explanations will vary, but should indicate that when rounding half-dollars up to dollars, the numbers will be greater, than when rounding pennies up to half dollars NJ Center for Teaching and Learning ~ 23 ~ www.njctl.org
NJ Center for Teaching and Learning ~ 24 ~ www.njctl.org