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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

what is microbiology
Agebe Reply
What is a cell
Odelana Reply
what is cell
Mohammed
how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
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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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