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Use a calculator, long division, or powers of 10 to change a fraction to a decimal
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Although they might seem intimidating at first, fractions and decimals are just two different ways of representing any number that’s less than 1. Fractions can be easily converted into their decimal form by dividing the number at the top (the numerator) by the number at the bottom (the denominator). If you don’t have a calculator on you, you can use long division to quickly figure out your answer. Whether you’re just starting out or you’d just like a quick refresher, this article covers all you need to know about converting fractions to decimals. Let’s dive in!
Things You Should Know
- To convert a fraction to a decimal, divide the numerator, or the top number in the fraction, by the denominator, which is the bottom number in the fraction.
- To use long division, place your denominator on the outside of the box and your numerator inside the box, then divide.
- For denominators that are factors of 10 (like 100 or 1,000), move the decimal to the left of the numerator as many places as you have zeros in the denominator.
Steps
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Put the numerator inside the division box with a decimal and a zero after it. To start the long division problem , draw a division box around your numerator and write the denominator to the left of the box. Place a decimal and a 0 after the numerator. [3] X Research source
- To convert : Place the 3 inside the division box and the 8 outside to the left of it. Place a decimal after the 3 and add a 0 to the end to get 3.0.
- To convert : Place the 1 inside the division box and the 3 outside to the left of it. Place a decimal after the 1 and add a 0 to the end to get 1.0.
- To convert : Place the 24 inside the division box and the 4 outside to the left of it. is larger than a whole number, so you don't need to add a decimal or a zero to the numerator.
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Ignore the decimal and divide the whole numerator by the denominator. Place a decimal at the top of the box directly over the decimal inside the box. Ignore the decimal inside the box and treat the number inside as a whole number (for example, 1.0 becomes 10). Write how many times you can put the denominator evenly into the numerator at the top of the box and find the remainder inside the box. [4] X Research source
- To convert : The 3.0 inside the division box becomes 30. 8 goes into 30 only 3 times, and . Place the 3 after the decimal at the top of the box, then , so 6 is left in the box.
- To convert : The 1.0 inside the box becomes 10. 3 goes into 10 only 3 times, and . Place a 3 after the decimal at the top of the box, and so 1 is left in the box.
- To convert : 4 goes into 27 only 6 times, and . Write the 6 before the decimal at the top of the box because 6 is the whole number. Now, we just need to find how much of is less than 1. At the bottom, write .
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Add another 0 to the end of the number in the box and drag it down to your answer. Place a 0 at the end of your numerator in the box. Draw an arrow from the 0 down to your answer at the bottom and add a 0 to the end of your answer so the number is large enough that you can divide it by the numerator. [5] X Research source
- To convert : You can’t divide 6 by 8, so add 0 after 3.0 to get 3.00. Drag the 0 down to your answer at the bottom to get 60, which you can now divide by 8.
- To convert : You can’t divide 1 by 3, so place a 0 after 1.0 inside the box to get 1.00. Draw an arrow from the new 0 down to your answer. Adding a 0 to the end of 1 equals 10, which you can now divide by 3.
- To convert : Place a decimal after 27 and add a 0 after it to get 27.0. Draw an arrow from the new 0 to your answer of 3 to get 30, which you can now divide by 4.
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Keep dividing until you get 0 or a repeating number. If you still have a remainder after dividing, place a 0 at the end of your numerator and your answer and divide them again. If you keep getting the same number or if you get 0 as your answer, you’re done with the problem. [6] X Research source
- To convert
:
You can put 8 into 60 just 7 times, and
. Add a 7 to the right of your answer at the top of the box. Then, find the remainder:
. Write a 0 after your numerator, then write a 0 after your answer at the bottom to get 40. You can put 8 into 40 evenly 5 times.
and
. Place the 5 to the right of your answer at the top, and you’re done!
- Final answer: 0.375
- To convert
:
You can put 3 into 10 just 3 times, and
. Add a 3 to the right of your answer at the top and subtract 9 from 10 to get 1. Notice a pattern? If you continue dividing, you’ll keep getting a remainder of 1 and continue to place 3 at the top of the box. Since you keep getting the same number, you’re done with the problem!
- Final answer: 0.333333 repeating
- To convert
:
4 goes into 30 just 7 times, and
. Place the 7 after the decimal at the top of the box. At the bottom, write
. Place a 0 after the 27.0 to get 27.00. Draw an arrow down to your answer, then place a 0 after the 2 to get 20. 4 goes into 20 evenly 5 times.
and
. Place the 5 at the top of the box. Since the answer is 0, you’re done with the problem!
- Final answer: 6.75
- To convert
:
You can put 8 into 60 just 7 times, and
. Add a 7 to the right of your answer at the top of the box. Then, find the remainder:
. Write a 0 after your numerator, then write a 0 after your answer at the bottom to get 40. You can put 8 into 40 evenly 5 times.
and
. Place the 5 to the right of your answer at the top, and you’re done!
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For repeating decimals, round it to the nearest hundredth or thousandth. If you have a number where the last digits repeat over and over, round it to the nearest hundredths or thousandths place. For example, if your answer is 0.375555, you can round it to the thousandth's place to get 0.376, or the hundredth's place to get 0.38. [7] X Research source
- If the number you’re rounding from is a 5 or higher, round up. If your number is 4 or lower, round down.
- If you don’t need a certain number of place values in your answer, draw a bar over the numbers that repeat to show that they’re going to repeat over and over forever. For example, 0.333 repeating can be also be written .
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Shift the decimal in the numerator to the left the number of zeroes in the denominator. Numbers with factors of 10 like 10, 100, 1,000, or 10,000 in the denominator can be easily turned into decimals. To get your answer, write down the numerator and move the decimal to the left the same number of spaces as you have zeroes in your denominator. [8] X Research source
- If your fraction is , write down 6.0 and move the decimal from the right of the number over 1 space to get 0.6 as your answer.
- If your fraction is , write down 54.0 and move the decimal 2 spaces to the left to get 0.54 as your answer.
- If your fraction is , write down 231.0. Since there are 4 zeroes in 10,000, move the decimal after 231 to the left 4 spaces to get 0.0231.
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Multiply the numerator by a common factor to get a power 10 denominator. Look for numbers with denominators that can be multiplied by another number to get a factor of 10. Multiply both the numerator and the denominator by that number to get a factor of 10 in the denominator, then move the decimal to the left the same number of spaces as you have zeroes in your denominator. [9] X Research source
- The 5 in can be multiplied by 2 to get 10. Write down 2.0. Because there’s 1 zero in 10, move the decimal to the left 1 place to get 0.2 as your answer.
- The 25 in can be multiplied by 4 to get 100. . Write down 36.0. Since there are 2 zeroes in 100, move the decimal to the left 2 spaces to get 0.36.
- To make your calculations faster, try writing down basic fraction/decimal equivalents like , , and on flashcards and quiz yourself regularly.
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In a fraction, the denominator, or the bottom number, is how many parts are in a whole. Each fraction has a numerator, or the top number, a slash, which goes between the numbers, and a denominator, which is the bottom number in the fraction. The denominator represents how many equal parts there are in the whole, like how many slices are in a whole pepperoni pizza.
- For example, a pizza might be cut into 8 slices. The denominator for the pizza would then be 8.
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In a fraction, the numerator, or the top number, is how many parts there are. While the denominator represents how many parts a whole is split into, the numerator represents how many equal parts are actually there, like how many slices are left in a whole pepperoni pizza after a group of people have eaten part of it. [10] X Research source
- For example, a pizza might only have 1 slice left out of its 8 slices. So, 1 piece of this pizza would be equal to the fraction .
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In a decimal, all the numbers to the right of the decimal represent less than a whole. Decimal numbers don’t have a slash to show how much of a whole number is left. Instead, all the numbers to the right of the decimal point represent the numbers that are less than a whole. [11] X Research source
- Decimals are also often read in a way that shows how similar they are to fractions. For example, 0.05 would commonly be read aloud as "five-hundredths," which is the same as , or “five-hundredths.”
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Practice Problems and Answers
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QuestionHow can I convert a fraction to a percent?This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.wikiHow Staff EditorStaff AnswerTo convert a fraction into a percent, first convert it into a decimal. For example, ½ = .5. Next, multiply the result by 100 to get a percent. Simply move the decimal point to the right 2 places. For example, .5 x 100 = 50%.
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QuestionHow do you turn a mixed number into a decimal?This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.wikiHow Staff EditorStaff AnswerFirst, convert the mixed number into an improper fraction. Multiply the whole number by the denominator, then add the result to the numerator to get the new numerator (e.g., 2 2/3 = 8/3). Divide the numerator by the denominator to get the decimal.
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QuestionCan you explain things in simpler terms?Community AnswerTo convert a fraction into a decimal, divide the top number by the bottom number.
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References
- ↑ https://www.purplemath.com/modules/percents2.htm
- ↑ https://www.purplemath.com/modules/percents2.htm
- ↑ https://edu.gcfglobal.org/en/multiplicationdivision/long-division/1/
- ↑ https://edu.gcfglobal.org/en/multiplicationdivision/long-division/1/
- ↑ https://edu.gcfglobal.org/en/multiplicationdivision/long-division/1/
- ↑ https://edu.gcfglobal.org/en/multiplicationdivision/long-division/1/
- ↑ https://www.purplemath.com/modules/percents2.htm
- ↑ https://www.greenemath.com/Prealgebra/39/DecimalDefinitionLesson.html
- ↑ https://www.greenemath.com/Prealgebra/39/DecimalDefinitionLesson.html
About This Article
Article Summary
X
To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25. After you divide, you can check your work by multiplying the decimal by the denominator to get the numerator. To learn how to convert fractions to decimals using power of 10 denominators, keep reading!
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