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A circle has radius 5 21 meters. Approximate its circumference and area.

  1. 220 147 m
  2. 550 3087 sq. m

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A circle has radius 10 33 inches. Approximate its circumference and area.

  1. 40 21 in.
  2. 200 693 sq.in.

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Key concepts

  • Convert a Fraction to a Decimal To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction.
  • Properties of Circles ... r is the length of the radius
    d is the length of the diameter
    The circumference is 2 π r . C = 2 π r
    The area is π r 2 . A = π r 2

Practice makes perfect

Convert Fractions to Decimals

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

In the following exercises, simplify the expression.

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using < or >.

In the following exercises, write each set of numbers in order from least to greatest.

3 5 , 9 16 , 0.55

0.55 , 9 16 , 3 5

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0.702 , 13 20 , 5 8

5 8 , 13 20 , 0.702

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−0.3 , 1 3 , 7 20

7 20 , 1 3 , 0.3

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−0.2 , 3 20 , 1 6

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3 4 , 7 9 , −0.7

7 9 , 3 4 , −0.7

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8 9 , 4 5 , −0.9

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Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

10 ( 25.1 43.8 )

−187

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62 ( 9.75 4.99 )

295.12

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3 4 ( 12.4 4.2 )

6.15

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5 12 ( 30.58 + 17.9 )

20.2

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10 ÷ 0.1 + ( 1.8 ) 4 ( 0.3 ) 2

107.11

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5 ÷ 0.5 + ( 3.9 ) 6 ( 0.7 ) 2

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( 37.1 + 52.7 ) ÷ ( 12.5 ÷ 62.5 )

449

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( 11.4 + 16.2 ) ÷ ( 18 ÷ 60 )

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( 1 5 ) 2 + ( 1.4 ) ( 6.5 )

9.14

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( 1 2 ) 2 + ( 2.1 ) ( 8.3 )

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9 10 · 8 15 + 0.25

−0.23

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Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

7 8 ( 103.48 ) + 1 1 2 ( 361 )

632.045

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5 16 ( 117.6 ) + 2 1 3 ( 699 )

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3.6 ( 9 8 2.72 )

−5.742

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Find the Circumference and Area of Circles

In the following exercises, approximate the circumference and area of each circle. If measurements are given in fractions, leave answers in fraction form.

radius = 5 in.

  1. 31.4 in
  2. 78.5 sq.in.

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radius = 9 ft.

  1. 56.52.ft.
  2. 254.34 sq.ft.

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radius = 46 cm

  1. 288.88 cm
  2. 6644.24 sq.cm

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radius = 18.6 m

  1. 116.808 m
  2. 1086.3144 sq.m

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radius = 7 10 mile

  1. 22 5 mile
  2. 77 50 sq.mile

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radius = 3 8 yard

  1. 33 14 yard
  2. 99 224 sq.yard

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diameter = 5 6 m

  1. 55 21 m
  2. 275 504 sq.m

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Everyday math

Kelly wants to buy a pair of boots that are on sale for 2 3 of the original price. The original price of the boots is $84.99 . What is the sale price of the shoes?

$56.66

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An architect is planning to put a circular mosaic in the entry of a new building. The mosaic will be in the shape of a circle with radius of 6 feet. How many square feet of tile will be needed for the mosaic? (Round your answer up to the next whole number.)

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Writing exercises

Is it easier for you to convert a decimal to a fraction or a fraction to a decimal? Explain.

Answers will vary.

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Describe a situation in your life in which you might need to find the area or circumference of a circle.

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Self check

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

.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Practice Key Terms 4

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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