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? ___

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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

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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

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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 _______________

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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

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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 SymbolsClasswork19)Put the correct symbol between each pair of numbers: >, <, =

a. 0.45 0.54

b. 0.43 0.430

c. 0.241 0.251

d. 4.23 0.423

e. 0.32 0.302

f. 0.671 0.618

g. 0.042 0.004

h. 13.05 13.5

i. 8.23 82.3

j. 0.479 0.439

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Homework

20) Put the correct symbol between each pair of numbers: >, <, =

a. 0.39 0.31

b. 0.73 0.073

c. 3.5 3.05

d. 6.2 6.200

e. 0.712 0.721

f. 0.9 0.901

g. 18.04 18.4

h. 0.043 0.05

i. 3.2 4

j. 0.643 0.609

Ordering DecimalsClasswork

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

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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

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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 ____________

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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 ____________

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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 ____________

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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 ____________

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Unit Review

Decimal Concepts Multiple Choice Questions

39)Which number represents sixty-nine thousandths?

a. 69,000b. 0.69c. 0.069d. 0.0069

40)Which number represents twenty-three and 15 hundredths?

a. 23.15b. 2,315c. 23.015d. 150.23

41)Which number represents five hundred fifty-two and two tenths?

a. 5,522b. 552.2c. 52.2d. 552.02

42)The number 90.78 is:

a. nine and seventy-eight hundredthsb. 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 thousandthsb. seven and eight hundredthsc. seven and eight thousandths d. seven and eight tenths

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45)Which digit is in the tenths place in the number 789.234?

a. 2b. 3c. 4d. 8

46)Which digit is in the thousandths place in the number 0.9384?

a. 8b. 4c. 0d. 3

47)Which digit is in the ones place in the number 529.673?

a. 9b. 6c. 7d. 2

48)Which digit is in the hundredths place in the number 123.4567?

a. 4b. 5c. 1d. 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. =

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53)0.006 ___ 0.016

a. > b. < c. =

54)Which number is the greatest?

a. 0.9998b. 9.998c. 98.88d. 9.899

55)Which number is the greatest?

a. 0.124b. 0.0012c. 0.0421d. 0.142

56)Which number is the least?

a. 3.7b. 7.3c. 7.03d. 0.73

57)Which number is the least?

a. 0.1b. 0.008 c. 0.08d. 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. $36.00b. $35.00c. $36.50 d. $37.00

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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. $101b. $91 c. $102d. $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. $3.00c. $3.80d. $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?

__________________

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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._________________

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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. _____________

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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.

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

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CW-HW Answer Key

1. 0.16; 0.40; 0.73; 0.502. a. 5 b. 0 c. 6 d. 7 e. 2 f. 3 g. 13. a. 9 b. 4 c. 1 d. 3 e. 9 f. 6 g. 7

4. 0.82; 0.57; 0.80; 0.125. a. 8 b. 3 c. nothing d. 6 e. 5 f. 4 g. 46. 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

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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 thousandths16.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. 0.00717.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

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7 8

c. 7,000.007 d. 4,730.003 e. 8.323 f. 651.4 g. 0.013 h. 45.99 i. 0.14 j. 6,543.2119.a. < b. = c. < d. > e. > f. > g. > h. < i. < j. >

20. a. > b. > c. > d. = e. < f. < g. < h. < i. < j. >

21.a. 0.034 b. 0.259 c. 0.03722. 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= 2.322223.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. 0.84026. 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=76.01227. 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 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

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e. 0.65332. a. $22.00 b. $7.00 c. $10.0033. 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. 4.7136. a. 53 b. 4 c. 54

d. 6 e. 137. a. $20.00 b. $7.00 c. $70.00 38. a. $46.30 b. $11.00 c. $15.00

Unit Review39.c40.a41.b42.d43.c 44.c45.a 46.a

47.a48.b49.b50.c51.a52.a53.b54.c

55.d56.d57.b58.a59.b60.c61.1.0; 4.4; .49

62. four hundred thirty- two and eight hundredths63.nine and sixty-four thousandths64.300.73165.9.9 66.8 < 8.3 < 8.65 < 8.9

< 967.0.8 < 0.809 < 0.82 <

0.827

68.6.0 > 0.6 > 0.05 > 0.006

69.0.13570.0.910 71.78.772.0.81

73.10074.78.7075.1.0

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. 80378. 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

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