<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses fractions of one percent. By the end of the module students should understand the meaning of a fraction of one percent and be able to make conversions involving fractions of one percent.

Section overview

  • Conversions Involving Fractions of One Percent
  • Conversions Involving Nonterminating Fractions

Conversions involving fractions of one percent

Percents such as 1 2 size 12{ { {1} over {2} } } {} %, 3 5 size 12{ { {3} over {5} } } {} %, 5 8 size 12{ { {5} over {8} } } {} %, and 7 11 size 12{ { {7} over {"11"} } } {} %, where 1% has not been attained, are fractions of 1%. This implies that

1 2 % = 1 2   of 1% size 12{ { {1} over {2} } %= { {1} over {2} } `"of 1%"} {}

3 5 % = 3 5   of 1% size 12{ { {3} over {5} } %= { {3} over {5} } `"of 1%"} {}

5 8 % = 5 8   of 1% size 12{ { {5} over {8} } %= { {5} over {8} } `"of 1%"} {}

7 11 % = 7 11   of 1% size 12{ { {7} over {"11"} } %= { {7} over {"11"} } `"of 1%"} {}

Since "percent" means "for each hundred," and "of" means "times," we have

1 2 % = 1 2 of 1% = 1 2 1 100 = 1 200 size 12{ { {1} over {2} } %= { {1} over {2} } `"of 1%"= { {1} over {2} } cdot { {1} over {"100"} } = { {1} over {"200"} } } {}

3 5 % = 3 5 of 1% = 3 5 1 100 = 3 500 size 12{ { {3} over {5} } %= { {3} over {5} } `"of 1%"= { {3} over {5} } cdot { {1} over {"100"} } = { {3} over {"500"} } } {}

5 8 % = 5 8 of 1% = 5 8 1 100 = 5 800 size 12{ { {5} over {8} } %= { {5} over {8} } `"of 1%"= { {5} over {8} } cdot { {1} over {"100"} } = { {5} over {"800"} } } {}

7 11 % = 7 11 of 1% = 7 11 1 100 = 7 1100 size 12{ { {7} over {"11"} } %= { {7} over {"11"} } `"of 1%"= { {7} over {"11"} } cdot { {1} over {"100"} } = { {7} over {"1100"} } } {}

Sample set a

Convert 2 3 size 12{ { {2} over {3} } } {} % to a fraction.

2 3 % = 2 3 of 1 % = 2 1 3 1 100 50 = 1 1 3 50 = 1 150

Got questions? Get instant answers now!

Convert 5 8 size 12{ { {5} over {8} } } {} % to a decimal.

5 8 % = 5 8 of 1 % = 5 8 1 100 = 0.625 0.01 = 0.00625

Got questions? Get instant answers now!

Practice set a

Convert 1 4 size 12{ { {1} over {4} } } {} % to a fraction.

1 400 size 12{ { {1} over {"400"} } } {}

Got questions? Get instant answers now!

Convert 3 8 size 12{ { {3} over {8} } } {} % to a fraction.

3 800 size 12{ { {3} over {"800"} } } {}

Got questions? Get instant answers now!

Convert 3 1 3 size 12{3 { {1} over {3} } } {} % to a fraction.

1 30 size 12{ { {1} over {"30"} } } {}

Got questions? Get instant answers now!

Conversions involving nonterminating fractions

We must be careful when changing a fraction of 1% to a decimal. The number 2 3 size 12{ { {2} over {3} } } {} , as we know, has a nonterminating decimal representation. Therefore, it cannot be expressed exactly as a decimal.

When converting nonterminating fractions of 1% to decimals, it is customary to express the fraction as a rounded decimal with at least three decimal places.

Converting a nonterminating fraction to a decimal

To convert a nonterminating fraction of 1% to a decimal:
  1. Convert the fraction as a rounded decimal.
  2. Move the decimal point two digits to the left and remove the percent sign.

Sample set b

Convert 2 3 size 12{ { {2} over {3} } } {} % to a three-place decimal.

  1. Convert 2 3 size 12{ { {2} over {3} } } {} to a decimal.

    Since we wish the resulting decimal to have three decimal digits, and removing the percent sign will account for two of them, we need to round 2 3 size 12{ { {2} over {3} } } {} to one place ( 2 + 1 = 3 ) size 12{ \( "2 "+" 1 "=" 3" \) } {} .

    2 3 % = 0 . 7 size 12{ { {2} over {3} } %=0 "." 7%} {} % to one decimal place. 2 3 = 0 . 6666 size 12{ left ( { {2} over {3} } =0 "." "6666" dotslow right )} {}

  2. Move the decimal point two digits to the left and remove the % sign. We'll need to add zeros to locate the decimal point in the correct location.

    2 3 % = 0 . 007 size 12{ { {2} over {3} } "% "=" 0" "." "007"} {} to 3 decimal places

Got questions? Get instant answers now!

Convert 5 4 11 size 12{5 { {4} over {"11"} } } {} % to a four-place decimal.

  1. Since we wish the resulting decimal to have four decimal places, and removing the percent sign will account for two, we to round 4 11 size 12{ { {4} over {"11"} } } {} to two places.

    5 4 11 % = 5 . 36 size 12{5 { {4} over {"11"} } %=5 "." "36"%} {} % to two decimal places. 4 11 = 0 . 3636 size 12{ left ( { {4} over {"11"} } =0 "." "3636" dotslow right )} {}

  2. Move the decimal point two places to the left and drop the percent sign.

    5 4 11 % = 0 . 0536 size 12{5 { {4} over {"11"} } %=5 "." "36"%} {} to four decimal places.

Got questions? Get instant answers now!

Convert 28 5 9 size 12{"28" { {5} over {9} } } {} % to a decimal rounded to ten thousandths.

  1. Since we wish the resulting decimal to be rounded to ten thousandths (four decimal places), and removing the percent sign will account for two, we need to round 5 9 size 12{ { {5} over {9} } } {} to two places.

    28 5 9 % = 28 . 56% size 12{"28" { {5} over {9} } %="28" "." "56"%} {} to two decimal places. 5 9 = 0 . 5555 size 12{ left ( { {5} over {9} } =0 "." "5555" dotslow right )} {}

  2. Move the decimal point to the left two places and drop the percent sign.

    28 5 9 % = 0 . 2856 size 12{"28" { {5} over {9} } %=0 "." "2856"} {} correct to ten thousandths.

Got questions? Get instant answers now!

Practice set b

Convert 7 9 size 12{ { {7} over {9} } } {} % to a three-place decimal.

0.008

Got questions? Get instant answers now!

Convert 51 5 11 % to a decimal rounded to ten thousandths.

0.5145

Got questions? Get instant answers now!

Exercises

Make the conversions as indi­cated.

Convert 3 4 size 12{ { {3} over {4} } } {} % to a fraction.

3 400 size 12{ { {3} over {"400"} } } {}

Got questions? Get instant answers now!

Convert 5 6 size 12{ { {5} over {6} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 1 9 size 12{ { {1} over {9} } } {} % to a fraction.

1 900 size 12{ { {1} over {"900"} } } {}

Got questions? Get instant answers now!

Convert 15 19 size 12{ { {"15"} over {"19"} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 5 4 size 12{ { {5} over {4} } } {} % to a fraction.

5 400 or 1 80 size 12{ { {5} over {"400"} } " or " { {1} over {"80"} } } {}

Got questions? Get instant answers now!

Convert 7 3 size 12{ { {7} over {3} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 1 6 7 size 12{1 { {6} over {7} } } {} % to a fraction.

13 700 size 12{ { {"13"} over {"700"} } } {}

Got questions? Get instant answers now!

Convert 2 5 16 size 12{2 { {5} over {"16"} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 25 1 4 size 12{"25" { {1} over {4} } } {} % to a fraction.

101 400 size 12{ { {"101"} over {"400"} } } {}

Got questions? Get instant answers now!

Convert 50 1 2 size 12{"50" { {1} over {2} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 72 3 5 size 12{"72" { {3} over {5} } } {} % to a fraction.

363 500 size 12{ { {"363"} over {"500"} } } {}

Got questions? Get instant answers now!

Convert 99 1 8 size 12{"99" { {1} over {8} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 136 2 3 size 12{"136" { {2} over {3} } } {} % to a fraction.

41 30 size 12{ { {"41"} over {"30"} } } {}

Got questions? Get instant answers now!

Convert 521 3 4 size 12{"521" { {3} over {4} } } {} % to a fraction.

Got questions? Get instant answers now!

Convert 10 1 5 size 12{"10" { {1} over {5} } } {} % to a decimal.

51 500 = 0 . 102 size 12{ { {"51"} over {"500"} } =0 "." "102"} {}

Got questions? Get instant answers now!

Convert 12 3 4 size 12{"12" { {3} over {4} } } {} % to a decimal.

Got questions? Get instant answers now!

Convert 3 7 8 size 12{3 { {7} over {8} } } {} % to a decimal.

31 800 = 0 . 03875 size 12{ { {"31"} over {"800"} } =0 "." "03875"} {}

Got questions? Get instant answers now!

Convert 7 1 16 size 12{7 { {1} over {"16"} } } {} % to a decimal.

Got questions? Get instant answers now!

Convert 3 7 size 12{ { {3} over {7} } } {} % to a three-place decimal.

0 . 004 size 12{0 "." "004"} {}

Got questions? Get instant answers now!

Convert 1 9 size 12{ { {1} over {9} } } {} % to a three-place decimal.

Got questions? Get instant answers now!

Convert 6 3 11 size 12{6 { {3} over {"11"} } } {} % to a four-place decimal.

0.0627

Got questions? Get instant answers now!

Convert 9 2 7 size 12{9 { {2} over {7} } } {} % to a four-place decimal.

Got questions? Get instant answers now!

Convert 24 5 21 size 12{"24" { {5} over {"21"} } } {} % to a three-place decimal.

0.242

Got questions? Get instant answers now!

Convert 45 8 27 size 12{"45" { {8} over {"27"} } } {} % to a three-place decimal.

Got questions? Get instant answers now!

Convert 11 16 17 size 12{"11" { {"16"} over {"17"} } } {} % to a four-place decimal.

0.1194

Got questions? Get instant answers now!

Convert 5 1 7 size 12{5 { {1} over {7} } } {} % to a three-place decimal.

Got questions? Get instant answers now!

Exercises for review

( [link] ) Write 8 8 8 8 8 size 12{"8 " cdot " 8 " cdot " 8 " cdot " 8 " cdot " 8"} {} using exponents.

8 5 size 12{8 rSup { size 8{5} } } {}

Got questions? Get instant answers now!

( [link] ) Convert 4 7 8 size 12{4 { {7} over {8} } } {} to an improper fraction.

Got questions? Get instant answers now!

( [link] ) Find the sum. 7 10 + 2 21 + 1 7 size 12{ { {7} over {"10"} } + { {2} over {"21"} } + { {1} over {7} } } {} .

197 210 size 12{ { {"197"} over {"210"} } } {}

Got questions? Get instant answers now!

( [link] ) Find the product. ( 4 . 21 ) ( 0 . 006 ) size 12{ \( 4 "." "21" \) \( 0 "." "006" \) } {} .

Got questions? Get instant answers now!

( [link] ) Convert 8.062 to a percent.

806 . 2 size 12{"806" "." 2%} {} %

Got questions? Get instant answers now!

Questions & Answers

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
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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