0.6___−0.7 Round Decimals

In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at

$3.279

per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay

$3.28

, because the final price would be rounded to the nearest cent. InWhole Numbers, we saw that we round numbers to get an approximate value when the exact value is not needed. Suppose we wanted to round

$2.72

to the nearest dollar. Is it closer to

$2

^{or to}

$3?

What if we wanted to round

$2.72

to the nearest ten cents; is it closer to

$2.70

^{or to}

$2.80?

The number lines inFigure 5.4can help us answer those questions.

Figure 5.4

ⓐ

We see that

2.72

is closer to

3

^{than to}

2.

^So,

2.72

rounded to the nearest whole number is

3.

ⓑ

We see that

2.72

is closer to

2.70

^than

2.80.

So we say that

2.72

rounded to the nearest tenth is

2.7.

Can we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.

HOW TO : :ROUND A DECIMAL.

Locate the given place value and mark it with an arrow.

Underline the digit to the right of the given place value.

Is this digit greater than or equal to

5?

◦ Yes - add

1

to the digit in the given place value.

◦ No - do not change the digit in the given place value

Rewrite the number, removing all digits to the right of the given place value.

Step 1.

Step 2.

Step 3.

Step 4.

EXAMPLE 5.9

Round

18.379

to the nearest hundredth.

Solution

Locate the hundredths place and mark it with an arrow.

Underline the digit to the right of the 7.

Because 9 is greater than or equal to 5, add 1 to the 7.

Rewrite the number, deleting all digits to the right of the hundredths place.

18.38 is 18.379 rounded to the nearest hundredth.

TRY IT : :5.17 Round to the nearest hundredth:

1.047.

TRY IT : :5.18 Round to the nearest hundredth:

9.173.

EXAMPLE 5.10

Round

18.379

to the nearest

ⓐ

^tenth

ⓑ

whole number.

Solution

ⓐ

Round 18.379 to the nearest tenth.

Locate the tenths place and mark it with an arrow.

Underline the digit to the right of the tenths digit.

Because 7 is greater than or equal to 5, add 1 to the 3.

Rewrite the number, deleting all digits to the right of the tenths place.

So, 18.379 rounded to the nearest tenth is 18.4.

ⓑ

Round 18.379 to the nearest whole number.

Locate the ones place and mark it with an arrow.

Underline the digit to the right of the ones place.

Since 3 is not greater than or equal to 5, do not add 1 to the 8.

Rewrite the number, deleting all digits to the right of the ones place.

So 18.379 rounded to the nearest whole number is 18.

TRY IT : :5.19 Round

6.582

to the nearest

ⓐ

^hundredth

ⓑ

^tenth

ⓒ

whole number.

TRY IT : :5.20 Round

15.2175

to the nearest

ⓐ

^thousandth

ⓑ

^hundredth

ⓒ

^tenth.

MEDIA : :ACCESS ADDITIONAL ONLINE RESOURCES

• Introduction to Decimal Notation (http://www.openstax.org/l/24decmlnotat)

• Write a Number in Decimal Notation from Words (http://www.openstax.org/l/24word2dcmlnot)

• Identify Decimals on the Number Line (http://www.openstax.org/l/24decmlnumline)

• Rounding Decimals (http://www.openstax.org/l/24rounddecml)

• Writing a Decimal as a Simplified Fraction (http://www.openstax.org/l/24decmlsimpfrac)

Practice Makes Perfect

Name Decimals

In the following exercises, name each decimal.

1.

5.5

^2.

7.8

^3.

5.01

4.

14.02

^5.

8.71

^6.

2.64

7.

0.002

^8.

0.005

^9.

0.381

10.

0.479

^11.

−17.9

^12.

−31.4

Write Decimals

In the following exercises, translate the name into a decimal number.

13.Eight and three hundredths 14.Nine and seven hundredths 15. Twenty-nine and eighty-one hundredths

16. Sixty-one and seventy-four

hundredths 17.Seven tenths 18.Six tenths

19.One thousandth 20.Nine thousandths 21.Twenty-nine thousandths 22.Thirty-five thousandths 23.Negative eleven and nine ten-

thousandths 24. Negative fifty-nine and two

ten-thousandths 25. Thirteen and three hundred

ninety-five ten thousandths 26. Thirty and two hundred seventy-nine thousandths Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

27.

1.99

^28.

5.83

^29.

15.7

30.

18.1

^31.

0.239

^32.

0.373

33.

0.13

^34.

0.19

^35.

0.011

36.

0.049

^37.

−0.00007

^38.

−0.00003

39.

6.4

^40.

5.2

^41.

7.05

42.

9.04

^43.

4.006

^44.

2.008

45.

10.25

^46.

12.75

^47.

1.324

48.

2.482

^49.

14.125

^50.

20.375

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

51.

0.8

^52.

0.3

^53.

−0.2

5.1 EXERCISES

54.

−0.9

^55.

3.1

^56.

2.7

57.

−2.5

^58.

−1.6

Order Decimals

In the following exercises, order each of the following pairs of numbers, using

< or>.

59.

0.9__0.6

^60.

0.7__0.8

^61.

0.37__0.63

62.

0.86__0.69

^63.

0.6__0.59

^64.

0.27__0.3

65.

0.91__0.901

^66.

0.415__0.41

^67.

−0.5__−0.3

68.

−0.1_−0.4

^69.

−0.62_−0.619

^70.

−7.31_−7.3

Round Decimals

In the following exercises, round each number to the nearest tenth.

71.

0.67

^72.

0.49

^73.

2.84

74.

4.63

In the following exercises, round each number to the nearest hundredth.

75.

0.845

^76.

0.761

^77.

5.7932

78.

3.6284

^79.

0.299

^80.

0.697

81.

4.098

^82.

7.096

In the following exercises, round each number to the nearest

ⓐ

^hundredth

ⓑ

^tenth

ⓒ

whole number.

83.

5.781

^84.

1.638

^85.

63.479

86.

84.281

Everyday Math

87.Salary IncreaseDanny got a raise and now makes

$58,965.95

a year. Round this number to the nearest:

ⓐ

^dollar

ⓑ

thousand dollars

ⓒ

ten thousand dollars.

88. New Car Purchase Selena’s new car cost

$23,795.95.

Round this number to the nearest:

ⓐ

^dollar

ⓑ

thousand dollars

ⓒ

ten thousand dollars.

89.Sales TaxHyo Jin lives in San Diego. She bought a refrigerator for

$1624.99

and when the clerk calculated the sales tax it came out to exactly

$142.186625.

Round the sales tax to the nearest

ⓐ

penny

ⓑ

^dollar.

90. Sales Tax Jennifer bought a

$1,038.99

^dining

room set for her home in Cincinnati. She calculated the sales tax to be exactly

$67.53435.

Round the sales tax to the nearest

ⓐ

^penny

ⓑ

^dollar.

Writing Exercises

91.How does your knowledge of money help you learn

about decimals? 92.Explain how you write “three and nine hundredths”

as a decimal.

93.Jim ran a

100-meter

^{race in}

12.32 seconds.

^Tim

ran the same race in

12.3 seconds.

Who had the faster time, Jim or Tim? How do you know?

94.Gerry saw a sign advertising postcards marked for sale at

“10 for 0.99¢.”

What is wrong with the advertised price?

Self Check

ⓐ

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success.

In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on.

Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

5.2

Decimal Operations

Learning Objectives

By the end of this section, you will be able to: