<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses percents. By the end of the module students should understand the relationship between ratios and percents and be able to make conversions between fractions, decimals, and percents.

Section overview

  • Ratios and Percents
  • The Relationship Between Fractions, Decimals, and Percents – Making Conversions

Ratios and percents

Ratio, percent

We defined a ratio as a comparison, by division, of two pure numbers or two like denominate numbers. A most convenient number to compare numbers to is 100. Ratios in which one number is compared to 100 are called percents . The word percent comes from the Latin word "per centum." The word "per" means "for each" or "for every," and the word "centum" means "hundred." Thus, we have the following definition.

Percent means “for each hundred," or "for every hundred."

The symbol % is used to represent the word percent.

Sample set a

The ratio 26 to 100 can be written as 26%. We read 26% as "twenty-six percent."

Got questions? Get instant answers now!

The ratio 165 100 size 12{ { {"165"} over {"100"} } } {} can be written as 165%.

We read 165% as "one hundred sixty-five percent."

Got questions? Get instant answers now!

The percent 38% can be written as the fraction 38 100 size 12{ { {"38"} over {"100"} } } {} .

Got questions? Get instant answers now!

The percent 210% can be written as the fraction 210 100 size 12{ { {"210"} over {"100"} } } {} or the mixed number 2 10 100 size 12{2 { {"10"} over {"100"} } } {} or 2.1.

Got questions? Get instant answers now!

Since one dollar is 100 cents, 25 cents is 25 100 size 12{ { {"25"} over {"100"} } } {} of a dollar. This implies that 25 cents is 25% of one dollar.

Got questions? Get instant answers now!

Practice set a

Write the ratio 16 to 100 as a percent.

16%

Got questions? Get instant answers now!

Write the ratio 195 to 100 as a percent.

195%

Got questions? Get instant answers now!

Write the percent 83% as a ratio in fractional form.

83 100 size 12{ { {"83"} over {"100"} } } {}

Got questions? Get instant answers now!

Write the percent 362% as a ratio in fractional form.

362 100 or 181 50 size 12{ { {"362"} over {"100"} } " or " { {"181"} over {"50"} } } {}

Got questions? Get instant answers now!

The relationship between fractions, decimals, and percents – making conversions

Since a percent is a ratio, and a ratio can be written as a fraction, and a fraction can be written as a decimal, any of these forms can be converted to any other.

Before we proceed to the problems in [link] and [link] , let's summarize the conversion techniques.

Conversion techniques – fractions, decimals, percents
To Convert a Fraction To Convert a Decimal To Convert a Percent
To a decimal: Divide the numerator by the denominator To a fraction: Read the decimal and reduce the resulting fraction To a decimal: Move the decimal point 2 places to the left and drop the % symbol
To a percent: Convert the fraction first to a decimal, then move the decimal point 2 places to the right and affix the % symbol. To a percent: Move the decimal point 2 places to the right and affix the % symbol To a fraction: Drop the % sign and write the number “over” 100. Reduce, if possible.

Sample set b

Convert 12% to a decimal.

12% = 12 100 = 0 . 12 size 12{"12% "= { {"12"} over {"100"} } =" 0" "." "12"} {}

Note that Twelve percent is equal to .12. this diagram shows that the decimal place in 12% moves two spaces to the left to convert to a decimal.

The % symbol is dropped, and the decimal point moves 2 places to the left.

Got questions? Get instant answers now!

Convert 0.75 to a percent.

0 . 75 = 75 100 = 75% size 12{0 "." "75"= { {"75"} over {"100"} } ="75"%} {}

Note that .75 percent is equal to 75%. this diagram shows that the decimal place in .75 moves two spaces to the right to convert to a percent.

The % symbol is affixed, and the decimal point moves 2 units to the right.

Got questions? Get instant answers now!

Convert 3 5 size 12{ { {3} over {5} } } {} to a percent.

We see in [link] that we can convert a decimal to a percent. We also know that we can convert a fraction to a decimal. Thus, we can see that if we first convert the fraction to a decimal, we can then convert the decimal to a percent.

3 5 .6 5 3.0 3 0 ̲ 0 or 3 5 = 0 . 6 = 6 10 = 60 100 = 60% size 12{ { {3} over {5} } =0 "." 6= { {6} over {"10"} } = { {"60"} over {"100"} } ="60"%} {}

Got questions? Get instant answers now!

Convert 42% to a fraction.

42% = 42 100 = 21 50 size 12{"42"%= { {"42"} over {"100"} } = { {"21"} over {"50"} } } {}

or

42% = 0 . 42 = 42 100 = 21 50 size 12{"42"%=0 "." "42"= { {"42"} over {"100"} } = { {"21"} over {"50"} } } {}

Got questions? Get instant answers now!

Practice set b

Convert 21% to a decimal.

0.21

Got questions? Get instant answers now!

Convert 461% to a decimal.

4.61

Got questions? Get instant answers now!

Convert 0.55 to a percent.

55%

Got questions? Get instant answers now!

Convert 5.64 to a percent.

564%

Got questions? Get instant answers now!

Convert 3 20 size 12{ { {3} over {"20"} } } {} to a percent.

15%

Got questions? Get instant answers now!

Convert 11 8 size 12{ { {"11"} over {8} } } {} to a percent

137.5%

Got questions? Get instant answers now!

Convert 3 11 size 12{ { {3} over {"11"} } } {} to a percent.

27 . 27 ¯ size 12{"27" "." {overline {"27"}} %} {} %

Got questions? Get instant answers now!

Exercises

For the following 12 problems, convert each decimal to a percent.

For the following 10 problems, convert each percent to a deci­mal.

For the following 14 problems, convert each fraction to a per­cent.

1 5 size 12{ { {1} over {5} } } {}

20%

Got questions? Get instant answers now!

3 5 size 12{ { {3} over {5} } } {}

Got questions? Get instant answers now!

5 8 size 12{ { {5} over {8} } } {}

62.5%

Got questions? Get instant answers now!

1 16 size 12{ { {1} over {"16"} } } {}

Got questions? Get instant answers now!

7 25 size 12{ { {7} over {"25"} } } {}

28%

Got questions? Get instant answers now!

16 45 size 12{ { {"16"} over {"45"} } } {}

Got questions? Get instant answers now!

27 55 size 12{ { {"27"} over {"55"} } } {}

49 . 09 ¯ size 12{"49" "." {overline {"09"}} } {} %

Got questions? Get instant answers now!

15 8 size 12{ { {"15"} over {8} } } {}

Got questions? Get instant answers now!

41 25 size 12{ { {"41"} over {"25"} } } {}

164%

Got questions? Get instant answers now!

6 4 5 size 12{6 { {4} over {5} } } {}

Got questions? Get instant answers now!

9 9 20 size 12{9 { {9} over {"20"} } } {}

945%

Got questions? Get instant answers now!

1 200 size 12{ { {1} over {"200"} } } {}

Got questions? Get instant answers now!

6 11 size 12{ { {6} over {"11"} } } {}

54 . 54 ¯ size 12{"54" "." {overline {"54"}} } {} %

Got questions? Get instant answers now!

35 27 size 12{ { {"35"} over {"27"} } } {}

Got questions? Get instant answers now!

For the following 14 problems, convert each percent to a fraction.

80%

4 5 size 12{ { {4} over {5} } } {}

Got questions? Get instant answers now!

25%

1 4 size 12{ { {1} over {4} } } {}

Got questions? Get instant answers now!

65%

13 20 size 12{ { {"13"} over {"20"} } } {}

Got questions? Get instant answers now!

12.5%

1 8 size 12{ { {1} over {8} } } {}

Got questions? Get instant answers now!

512.5%

41 8 or   5 1 8 size 12{ { {"41"} over {8} } " or "5 { {1} over {8} } } {}

Got questions? Get instant answers now!

9 . 9 _ %

1 10 size 12{ { {1} over {"10"} } } {}

Got questions? Get instant answers now!

22 . 2 _ %

2 9 size 12{ { {2} over {9} } } {}

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the quotient. 40 54 ÷ 8 7 21 size 12{ { {"40"} over {"54"} } +8 { {7} over {"21"} } } {} .

4 45 size 12{ { {4} over {"45"} } } {}

Got questions? Get instant answers now!

( [link] ) 3 8 size 12{ { {3} over {8} } } {} of what number is 2 2 3 size 12{2 { {2} over {3} } } {} ?

Got questions? Get instant answers now!

( [link] ) Find the value of 28 15 + 7 10 5 12 size 12{ { {"28"} over {"15"} } + { {7} over {"10"} } - { {5} over {"12"} } } {} .

129 60 or   2 9 60 = 2 3 20 size 12{ { {"129"} over {"60"} } " or "2 { {9} over {"60"} } =2 { {3} over {"20"} } } {}

Got questions? Get instant answers now!

( [link] ) Round 6.99997 to the nearest ten thousandths.

Got questions? Get instant answers now!

( [link] ) On a map, 3 inches represent 40 miles. How many inches represent 480 miles?

36 inches

Got questions? Get instant answers now!

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
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
Wekolamo Reply
please i need answer
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).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
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
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
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.
Samuel
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
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask