1. Home
  2. Contemporary math applications
  3. Helpful topics
  4. Decimals
  5. Decimals: converting a fraction

8.6 Decimals: converting a fraction to a decimal

<< Chapter < Page
  Contemporary math applications   Page 1 / 1
Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to convert a fraction to a decimal. By the end of the module students should be able to convert a fraction to a decimal.

Now that we have studied and practiced dividing with decimals, we are also able to convert a fraction to a decimal. To do so we need only recall that a fraction bar can also be a division symbol. Thus, 3 4 size 12{ { {3} over {4} } } {} not only means "3 objects out of 4," but can also mean "3 divided by 4."

Sample set a

Convert the following fractions to decimals. If the division is nonterminating, round to two decimal places.

3 4 size 12{ { {3} over {4} } } {} . Divide 3 by 4.

.75 4 3.00 2 8   ̲ 20 20 ̲ 0

Thus, 3 4 = 0 . 75 size 12{ { {3} over {4} } =0 "." "75"} {} .

1 5 size 12{ { {1} over {5} } } {} Divide 1 by 5.

.2 5 1.0 1.0 ̲ 0

Thus, 1 5 = 0 . 2 size 12{ { {1} over {5} } =0 "." 2} {}

5 6 size 12{ { {5} over {6} } } {} . Divide 5 by 6.

Long division. 5 divided by 6 ends in a recurring remainder. The quotient is .833. The recurring remainder indicates that the division is nonterminating.

5 6 = 0 . 833 ⋯ size 12{ { {5} over {6} } =0 "." "833" dotsaxis } {} We are to round to two decimal places.

Thus, 5 6 = 0 . 83 size 12{ { {5} over {6} } =0 "." "83"} {} to two decimal places.

5 1 8 size 12{5 { {1} over {8} } } {} . Note that 5 1 8 = 5 + 1 8 size 12{5 { {1} over {8} } =5+ { {1} over {8} } } {} .

Convert 1 8 size 12{ { {1} over {8} } } {} to a decimal.

.125 8 1.000   8     ̲ 20   16   ̲ 40 40 ̲ 0

1 8 = . 125 size 12{ { {1} over {8} } = "." "125"} {}

Thus, 5 1 8 = 5 + 1 8 = 5 + . 125 = 5 . 125 size 12{5 { {1} over {8} } =5+ { {1} over {8} } =5+ "." "125"=5 "." "125"} {} .

0 . 16 1 4 size 12{0 "." "16" { {1} over {4} } } {} . This is a complex decimal.

Note that the 6 is in the hundredths position.

The number 0 . 16 1 4 size 12{0 "." "16" { {1} over {4} } } {} is read as "sixteen and one-fourth hundredths."

0 . 16 1 4 = 16 1 4 100 = 16 ⋅ 4 + 1 4 100 = 65 4 100 1 = 65 13 4 ⋅ 1 100 20 = 13 ⋅ 1 4 ⋅ 20 = 13 80 size 12{0 "." "16" { {1} over {4} } = { {"16" { {1} over {4} } } over {"100"} } = { { { {"16" cdot 4+1} over {4} } } over {"100"} } = { { { {"65"} over {4} } } over { { {"100"} over {1} } } } = { { {"65"} cSup { size 8{"13"} } } over {4} } cdot { {1} over { {"100"} cSub { size 8{"20"} } } } = { {"13" cdot 1} over {4 cdot "20"} } = { {"13"} over {"80"} } } {}

Now, convert 13 80 size 12{ { {"13"} over {"80"} } } {} to a decimal.

.1625 80 13.0000 8 0       ̲ 5 00     4 80     ̲ 200   160   ̲ 400 400 ̲ 0

Thus, 0 . 16 1 4 = 0 . 1625 size 12{0 "." "16" { {1} over {4} } =0 "." "1625"} {} .

Practice set a

Convert the following fractions and complex decimals to decimals (in which no proper fractions appear). If the divison is nonterminating, round to two decimal places.

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

0.25

1 25 size 12{ { {1} over {"25"} } } {}

0.04

1 6 size 12{ { {1} over {6} } } {}

0.17

15 16 size 12{ { {"15"} over {"16"} } } {}

0.9375

0 . 9 1 2 size 12{0 "." 9 { {1} over {2} } } {}

0.95

8 . 0126 3 8 size 12{8 "." "0126" { {3} over {8} } } {}

8.0126375

Exercises

For the following 30 problems, convert each fraction or complex decimal number to a decimal (in which no proper fractions appear).

1 2 size 12{ { {1} over {2} } } {}

0.5

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

7 8 size 12{ { {7} over {8} } } {}

0.875

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

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

0.6

2 5 size 12{ { {2} over {5} } } {}

1 25 size 12{ { {1} over {"25"} } } {}

0.04

3 25 size 12{ { {3} over {"25"} } } {}

1 20 size 12{ { {1} over {"20"} } } {}

0.05

1 15 size 12{ { {1} over {"15"} } } {}

1 50 size 12{ { {1} over {"50"} } } {}

0.02

1 75 size 12{ { {1} over {"75"} } } {}

1 3 size 12{ { {1} over {3} } } {}

0 . 3 ¯ size 12{0 "." {overline {3}} } {}

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

3 16 size 12{ { {3} over {"16"} } } {}

0.1875

9 16 size 12{ { {9} over {"16"} } } {}

1 27 size 12{ { {1} over {"27"} } } {}

0 . 0 37 ¯ size 12{0 "." 0 {overline {"37"}} } {}

5 27 size 12{ { {5} over {"27"} } } {}

7 13 size 12{ { {7} over {"13"} } } {}

0 . 538461 ¯ size 12{0 "." {overline {"538461"}} } {}

9 14 size 12{ { {9} over {"14"} } } {}

7 2 3 size 12{7 { {2} over {3} } } {}

7 . 6 ¯ size 12{7 "." {overline {6}} } {}

8 5 16 size 12{8 { {5} over {"16"} } } {}

1 2 15 size 12{1 { {2} over {"15"} } } {}

1 . 1 3 ¯ size 12{1 "." 1 {overline {3}} } {}

65 5 22 size 12{"65" { {5} over {"22"} } } {}

101 6 25 size 12{"101" { {6} over {"25"} } } {}

101.24

0 . 1 1 2 size 12{0 "." 1 { {1} over {2} } } {}

0 . 24 1 8 size 12{0 "." "24" { {1} over {8} } } {}

0.24125

5 . 66 2 3 size 12{5 "." "66" { {2} over {3} } } {}

810 . 3106 5 16 size 12{"810" "." "3106" { {5} over {"16"} } } {}

810.31063125

4 . 1 1 9 size 12{4 "." 1 { {1} over {9} } } {}

For the following 18 problems, convert each fraction to a decimal. Round to five decimal places.

1 9 size 12{ { {1} over {9} } } {}

0.11111

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

3 9 size 12{ { {3} over {9} } } {}

0.33333

4 9 size 12{ { {4} over {9} } } {}

5 9 size 12{ { {5} over {9} } } {}

0.55556

6 9 size 12{ { {6} over {9} } } {}

7 9 size 12{ { {7} over {9} } } {}

0.77778

8 9 size 12{ { {8} over {9} } } {}

1 11 size 12{ { {1} over {"11"} } } {}

0.09091

2 11 size 12{ { {2} over {"11"} } } {}

3 11 size 12{ { {3} over {"11"} } } {}

0.27273

4 11 size 12{ { {4} over {"11"} } } {}

5 11 size 12{ { {5} over {"11"} } } {}

0.45455

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

7 11 size 12{ { {7} over {"11"} } } {}

0.63636

8 11 size 12{ { {8} over {"11"} } } {}

9 11 size 12{ { {9} over {"11"} } } {}

0.81818

10 11 size 12{ { {"10"} over {"11"} } } {}

Calculator problems

For the following problems, use a calculator to convert each fraction to a decimal. If no repeating pattern seems to exist, round to four decimal places.

16 125 size 12{ { {"16"} over {"125"} } } {}

0.128

85 311 size 12{ { {"85"} over {"311"} } } {}

192 197 size 12{ { {"192"} over {"197"} } } {}

0.9746

1 1469 size 12{ { {1} over {"1469"} } } {}

4 21 , 015 size 12{ { {4} over {"21","015"} } } {}

0.0002

81 , 426 106 , 001 size 12{ { {"81","426"} over {"106","001"} } } {}

16 , 501 426 size 12{ { {"16","501"} over {"426"} } } {}

38.7347

Exercises for review

( [link] ) Round 2,105,106 to the nearest hundred thousand.

( [link] ) 8 5 size 12{ { {8} over {5} } } {} of what number is 3 2 size 12{ { {3} over {2} } } {} ?

15 16 size 12{ { {"15"} over {"16"} } } {}

( [link] ) Arrange 1 9 16 size 12{1 { {9} over {"16"} } } {} , 1 5 8 size 12{1 { {5} over {8} } } {} , and 1 7 12 size 12{1 { {7} over {"12"} } } {} in increasing order.

( [link] ) Convert the complex decimal 3 . 6 5 4 size 12{3 "." 6 { {5} over {4} } } {} to a fraction.

3 29 40 size 12{3 { {"29"} over {"40"} } } {} or 3.725

( [link] ) Find the quotient. 30 ÷ 1 . 1 size 12{"30" div 1 "." 1} {} .

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask