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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

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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

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Practice set a

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

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

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

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

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

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

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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

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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.

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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.

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Practice set b

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

0.008

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

0.5145

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Exercises

Make the conversions as indi­cated.

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

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

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

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

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

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

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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"} } } {}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

0.0627

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

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

0.242

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

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

0.1194

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

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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} } } {}

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

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( [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"} } } {}

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

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( [link] ) Convert 8.062 to a percent.

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

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
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..
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Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
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what is the stm
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is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
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What is STMs full form?
LITNING
scanning tunneling microscope
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how nano science is used for hydrophobicity
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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what is differents between GO and RGO?
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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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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what is Nano technology ?
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write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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Adin Reply
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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