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 ______
NJ Center for Teaching and Learning ~ 4 ~ www.njctl.org b. Nine hundred thirty-three and seven tenths ______
c. Two thousand, five hundred three and twenty hundredths ______
d. Seventy-three thousandths ______
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
d. 4.23 0.423
b. 0.43 0.430
e. 0.32 0.302
c. 0.241 0.251 f. 0.671 0.618
NJ Center for Teaching and Learning ~ 6 ~ www.njctl.org g. 0.042 0.004 i. 8.23 82.3
h. 13.05 13.5 j. 0.479 0.439
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
NJ Center for Teaching and Learning ~ 7 ~ www.njctl.org 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 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
NJ Center for Teaching and Learning ~ 8 ~ www.njctl.org d. 0.1 0.101 0.011 0.1011
e. 67.21 76.012 67.012 67.201
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 ______
NJ Center for Teaching and Learning ~ 9 ~ www.njctl.org c. 631.083 ______
d. 5.961 ______
e. 4.712 ______
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 ______
NJ Center for Teaching and Learning ~ 10 ~ www.njctl.org b. $0.80, $1.20, $1.99 ______
c. $14.45, $10.10, $19.99 ______
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 ______
NJ Center for Teaching and Learning ~ 11 ~ www.njctl.org 36) Round each of the following to the nearest whole number (one):
a. 52.8097 ______
b. 3.9823 ______
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 ______
NJ Center for Teaching and Learning ~ 12 ~ www.njctl.org c. $6.80, $3.21, $5.01 ______
NJ Center for Teaching and Learning ~ 13 ~ 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 ~ 14 ~ 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 ~ 15 ~ 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 ~ 16 ~ 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 ~ 17 ~ 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 ~ 18 ~ 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 ~ 19 ~ 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 ~ 20 ~ www.njctl.org CW-HW Answer Key
1. 0.16; 0.40; 0.73; 0.50 4. 0.82; 0.57; 0.80; 0.12 2. a. 5 5. a. 8 b. 0 b. 3 c. 6 c. nothing d. 7 d. 6 e. 2 e. 5 f. 3 f. 4 g. 1 g. 4 3. a. 9 6. a. 1 b. 4 b.0 c. 1 c. 8 d. 3 d. 9 e. 9 e. 4 f. 6 f. 9 g. 7 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.
NJ Center for Teaching and Learning ~ 21 ~ www.njctl.org 3.2 3.35 3.5 3.85
12. 10.25 10.5 10.75
13. 7.1 7.3 7.45 7.7
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
NJ Center for Teaching and Learning ~ 22 ~ www.njctl.org 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 1) 18.a. 315.7 2) b. 9,605.73 3) c. 7,000.007 4) d. 4,730.003 5) e. 8.323 6) f. 651.4 7) g. 0.013 8) h. 45.99 9) i. 0.14 10) j. 6,543.21 11)19.a. < 21)20. a. > 12) b. = 22) b. > 13) c. < 23) c. > 14) d. > 24) d. = 15) e. > 25) e. < 16) f. > 26) f. < 17) g. > 27) g. < 18) h. < 28) h. < 19) i. < 29) i. < 20) j. > 30) j. > 31)21.a. 0.034 32) b. 0.259 33) c. 0.037 34) 22. a. circle=11.2907; underline=11.9720 35) b. circle= 257.23; underline= 275.32 36) c. circle= 0.375; underline= 0.85 37) d. circle= 0.007 underline= 0.3 38) e. circle= 2.2223 underline= 2.3222 39)23.a. 0.04 < 0.405 < 0.45 < 0.5 40) b. 3.062 < 3.09 < 3.2 < 3.7 41)24.a. 81 > 0.81 > 0.081 > 0.0008 42) b. 9.327 > 9.32 > 9.3 >9.01 43)25. a. 0.762 44) b. 0.610 45) c. 0.840 46)26. a. circle= 0.1112 underline= 0.2221 47) b. circle= 3324.9 underline= 3453.7 48) c. circle= 0.658 underline= 0.865 49) d. circle= 0.011 underline= 0.1011 50) e. circle= 67.012 underline=76.012
NJ Center for Teaching and Learning ~ 23 ~ www.njctl.org 51)27. a. 9.008 < 9.03 < 9.3 < 9.41 52) b. 0.401 < 0.47 < 0.56 < 0.6 53)28. a. 7.59 > 7.54 > 7.037 > 7.03 54) b. 7 > 0.7 > 0.07 > 0.007 55)29. Rounding is used to make numbers easier to work with, but results are not precise. 56)30. a. 43.9 67) b. $7.00 78)36. a. 53 57) b. 0.8 68) c. $10.00 79) b. 4 58) c. 631.1 69)33. a. $15.50 80) c. 54 59) d. 6.0 70) b. $4.00 81) d. 6 60) e. 4.7 71) c. $44.60 82) e. 1 61)31. a. 52.810 72)34. answers will vary 83)37. a. $20.00 62) b. 3.982 73)35. a. 43.88 84) b. $7.00 63) c. 54.006 74) b. 0.80 85) c. $70.00 64) d. 6.050 75) c. 631.08 86)38. a. $46.30 65) e. 0.653 76) d. 5.96 87) b. $11.00 66)32. a. $22.00 77) e. 4.71 88) c. $15.00 89) Unit Review 39.c 47.a 55.d 40.a 48.b 56.d 41.b 49.b 57.b 42.d 50.c 58.a 43.c 51.a 59.b 44.c 52.a 60.c 45.a 53.b 61.1.0; 4.4; .49 46.a 54.c 62. 63.four hundred thirty- two and eight hundredths 64.nine and sixty-four thousandths 65.300.731 69.6.0 > 0.6 > 0.05 > 74.100 66.9.9 0.006 75.78.70 67.8 < 8.3 < 8.65 < 8.9 70.0.135 76.1.0 < 9 71.0.910 68.0.8 < 0.809 < 0.82 < 72.78.7 0.827 73.0.81 77. 78.a. 6 6.2 6.55 6.8 7 79. 80. 81.b. 6 82. c. answers will vary 83.77. a. 802.802 84. b. eight hundred two and eight tenths 85. c. 803 86.78. a. $17.00
NJ Center for Teaching and Learning ~ 24 ~ www.njctl.org 87. b. $17.50 88. 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 89. 90. 91. 92.
NJ Center for Teaching and Learning ~ 25 ~ www.njctl.org 93.
NJ Center for Teaching and Learning ~ 26 ~ www.njctl.org