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By the end of this section, you will be able to:
  • Use the definition of percent
  • Convert percents to fractions and decimals
  • Convert decimals and fractions to percents

Before you get started, take this readiness quiz.

  1. Translate “the ratio of 33 to 5” into an algebraic expression.
    If you missed this problem, review Evaluate, Simplify and Translate Expressions .
  2. Write 3 5 as a decimal.
    If you missed this problem, review Decimals and Fractions .
  3. Write 0.62 as a fraction.
    If you missed this problem, review Decimals .

Use the definition of percent

How many cents are in one dollar? There are 100 cents in a dollar. How many years are in a century? There are 100 years in a century. Does this give you a clue about what the word “percent” means? It is really two words, “per cent,” and means per one hundred. A percent    is a ratio whose denominator is 100 . We use the percent symbol %, to show percent.


A percent is a ratio whose denominator is 100 .

According to data from the American Association of Community Colleges ( 2015 ) , about 57% of community college students are female. This means 57 out of every 100 community college students are female, as [link] shows. Out of the 100 squares on the grid, 57 are shaded, which we write as the ratio 57 100 .

The figure shows a hundred flat with 57 units shaded.
Among every 100 community college students, 57 are female.

Similarly, 25% means a ratio of 25 100 , 3% means a ratio of 3 100 and 100% means a ratio of 100 100 . In words, "one hundred percent" means the total -100%- is 100 100 , and since 100 100 = 1 , we see that 100% means 1 whole.

According to the Public Policy Institute of California ( 2010 ) , 44% of parents of public school children would like their youngest child to earn a graduate degree. Write this percent as a ratio.


The amount we want to convert is 44%. 44%
Write the percent as a ratio. Remember that percent means per 100. 44 100
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Write the percent as a ratio.

According to a survey, 89% of college students have a smartphone.

89 100

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Write the percent as a ratio.

A study found that 72% of U.S. teens send text messages regularly.

72 100

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In 2007 , according to a U.S. Department of Education report, 21 out of every 100 first-time freshmen college students at 4-year public institutions took at least one remedial course. Write this as a ratio and then as a percent.


The amount we want to convert is 21 out of every 100 .

Write as a ratio. 21 100
Convert the 21 per 100 to percent. 21%
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Write as a ratio and then as a percent: The American Association of Community Colleges reported that 62 out of 100 full-time community college students balance their studies with full-time or part time employment.

62 100 , 62%

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Write as a ratio and then as a percent: In response to a student survey, 41 out of 100 Santa Ana College students expressed a goal of earning an Associate's degree or transferring to a four-year college.

41 100 , 41%

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Convert percents to fractions and decimals

Since percents are ratios, they can easily be expressed as fractions. Remember that percent    means per 100 , so the denominator of the fraction is 100 .

Convert a percent to a fraction.

  1. Write the percent as a ratio with the denominator 100 .
  2. Simplify the fraction if possible.

Questions & Answers

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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how did you get the value of 2000N.What calculations are needed to arrive at it
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how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 1

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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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