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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?

Questions & Answers

I'm interested in biological psychology and cognitive psychology
Tanya Reply
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sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
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Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
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ARC
A child is a member of community not society elucidate ?
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Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
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namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
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explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
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I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
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Jonathan
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Jonathan
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interpersonal relationships
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What would be the best educational aid(s) for gifted kids/savants?
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Saurabh
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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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