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Decimals: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Decimals" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Reading and Writing Decimals ((Reference))

Exercise 1

The decimal digit that appears two places to the right of the decimal point is in the

               
position.

Solution

hundredths

Exercise 2

The decimal digit that appears four places to the right of the decimal point is in the

               
position.

For problems 3-8, read each decimal by writing it in words.

Exercise 3

7.2

Solution

seven and two tenths

Exercise 4

8.105

Exercise 5

16.52

Solution

sixteen and fifty-two hundredths

Exercise 6

5.9271

Exercise 7

0.005

Solution

five thousandths

Exercise 8

4.01701

For problems 9-13, write each decimal using digits.

Exercise 9

Nine and twelve-hundredths.

Solution

9.12

Exercise 10

Two and one hundred seventy-seven thousandths.

Exercise 11

Fifty-six and thirty-five ten-thousandths.

Solution

56.0035

Exercise 12

Four tenths.

Exercise 13

Four thousand eighty-one millionths.

Solution

0.004081

Converting a Decimal to a Fraction ((Reference))

For problem 14-20, convert each decimal to a proper fraction or a mixed number.

Exercise 14

1.07

Exercise 15

58.63

Solution

85631008563100 size 12{"85" { {"63"} over {"100"} } } {}

Exercise 16

0.05

Exercise 17

0.14230.1423 size 12{0 "." "14" { {2} over {3} } } {}

Solution

11751175 size 12{ { {"11"} over {"75"} } } {}

Exercise 18

1.09181.0918 size 12{1 "." "09" { {1} over {8} } } {}

Exercise 19

4.011274.01127 size 12{4 "." "01" { {1} over {"27"} } } {}

Solution

4767547675 size 12{4 { {7} over {"675"} } } {}

Exercise 20

9.11199.1119 size 12{9 "." "11" { {1} over {9} } } {}

Rounding Decimals ((Reference))

For problems 21-25, round each decimal to the specified position.

Exercise 21

4.087 to the nearest hundredth.

Solution

4.09

Exercise 22

4.087 to the nearest tenth.

Exercise 23

16.5218 to the nearest one.

Solution

17

Exercise 24

817.42 to the nearest ten.

Exercise 25

0.9811602 to the nearest one.

Solution

1

Addition, Subtraction, Multiplication and Division of Decimals, and Nonterminating Divisions ((Reference),(Reference),(Reference),(Reference))

For problem 26-45, perform each operation and simplify.

Exercise 26

7.10+2.987.10+2.98 size 12{7 "." "10"+2 "." "98"} {}

Exercise 27

14.0075.06114.0075.061 size 12{"14" "." "007" - 5 "." "061"} {}

Solution

8.946

Exercise 28

1.28.61.28.6 size 12{1 "." 2 cdot 8 "." 6} {}

Exercise 29

41.80.1941.80.19 size 12{"41" "." 8 cdot 0 "." "19"} {}

Solution

7.942

Exercise 30

57.51÷2.757.51÷2.7 size 12{"57" "." "51" div 2 "." 7} {}

Exercise 31

0.54003÷18.0010.54003÷18.001 size 12{0 "." "54003" div "18" "." "001"} {}

Solution

0.03

Exercise 32

32,051.3585÷23,006.999932,051.3585÷23,006.9999 size 12{"32,051" "." "3585" div "23","006" "." "9999"} {}

Exercise 33

1001,816.0011001,816.001 size 12{"100" cdot 1,"816" "." "001"} {}

Solution

181,600.1

Exercise 34

1,0001,816.0011,0001,816.001 size 12{1,"000" cdot 1,"816" "." "001"} {}

Exercise 35

10.0000.1410.0000.14 size 12{"10" "." "000" cdot 0 "." "14"} {}

Solution

1.4

Exercise 36

0.135888÷16.9860.135888÷16.986 size 12{0 "." "135888" div "16" "." "986"} {}

Exercise 37

150.79÷100150.79÷100 size 12{"150" "." "79" div "100"} {}

Solution

1.5079

Exercise 38

4.119÷10,0004.119÷10,000 size 12{4 "." "119" div "10","000"} {}

Exercise 39

42.7÷1842.7÷18 size 12{"42" "." 7 div "18"} {}

Solution

2.372¯2.372¯ size 12{2 "." "37" {overline {2}} } {}

Exercise 40

6.9÷126.9÷12 size 12{6 "." 9 div "12"} {}

Exercise 41

0.014÷47.60.014÷47.6 size 12{0 "." "014" div "47" "." 6} {}. Round to three decimal places.

Solution

0.000

Exercise 42

8.8÷198.8÷19 size 12{8 "." 8 div "19"} {}. Round to one decimal place.

Exercise 43

1.1÷91.1÷9 size 12{1 "." 1 div 9} {}

Solution

0.12¯0.12¯ size 12{0 "." {overline {"12"}} } {}

Exercise 44

1.1÷9.91.1÷9.9 size 12{1 "." 1 div 9 "." 9} {}

Exercise 45

30÷11.130÷11.1 size 12{"30" div "11" "." 1} {}

Solution

2.702¯2.702¯ size 12{2 "." {overline {"702"}} } {}

Converting a Fraction to a Decimal ((Reference))

For problems 46-55, convert each fraction to a decimal.

Exercise 46

3838 size 12{ { {3} over {8} } } {}

Exercise 47

4310043100 size 12{ { {"43"} over {"100"} } } {}

Solution

0.43

Exercise 48

821000821000 size 12{ { {"82"} over {"1000"} } } {}

Exercise 49

947947 size 12{9 { {4} over {7} } } {}

Solution

9.571428¯9.571428¯ size 12{9 "." {overline {"571428"}} } {}

Exercise 50

85168516 size 12{8 { {5} over {"16"} } } {}

Exercise 51

1.3131.313 size 12{1 "." 3 { {1} over {3} } } {}

Solution

1.3¯1.3¯ size 12{1 "." {overline {3}} } {}

Exercise 52

25.62325.623 size 12{"25" "." 6 { {2} over {3} } } {}

Exercise 53

125.12518125.12518 size 12{"125" "." "125" { {1} over {8} } } {}

Solution

125.125125 (not repeating)

Exercise 54

9.11199.1119 size 12{9 "." "11" { {1} over {9} } } {}

Exercise 55

0.0560.056 size 12{0 "." 0 { {5} over {6} } } {}

Solution

0.083¯0.083¯ size 12{0 "." "08" {overline {3}} } {}

Combinations of Operations with Decimals and Fractions ((Reference))

For problems 56-62, perform each operation.

Exercise 56

580.25580.25 size 12{ { {5} over {8} } cdot 0 "." "25"} {}

Exercise 57

3161.363161.36 size 12{ { {3} over {"16"} } cdot 1 "." "36"} {}

Solution

0.255

Exercise 58

3512+1.753512+1.75 size 12{ { {3} over {5} } cdot left ( { {1} over {2} } +1 "." "75" right )} {}

Exercise 59

7254+0.307254+0.30 size 12{ { {7} over {2} } cdot left ( { {5} over {4} } +0 "." "30" right )} {}

Solution

5.425

Exercise 60

19.375÷4.375111619.375÷4.3751116 size 12{"19" "." "375" div left (4 "." "375" - 1 { {1} over {"16"} } right )} {}

Exercise 61

156022.6¯+314156022.6¯+314 size 12{ { {"15"} over {"602"} } cdot left (2 "." {overline {6}} +3 { {1} over {4} } right )} {}

Solution

0.09343

Exercise 62

41318÷5314+352141318÷5314+3521 size 12{4 { {"13"} over {"18"} } div left (5 { {3} over {"14"} } +3 { {5} over {"21"} } right )} {}

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