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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
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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