PDF download Download Article PDF download Download Article

Converting numbers between percents, fractions, and decimals is a necessary basic math skill. The concepts are quite simple once you learn them. Not only will knowing how to convert small numbers help you on your test, but it is also useful for financial calculations.

Method 1
Method 1 of 3:

Converting Percents

PDF download Download Article
  1. Unless otherwise noted, in a percent, the decimal point comes at the end of the last number. For example, envision that 75% actually looks like 75.0%. Moving the decimal point two places to the left converts the percent to a decimal. This is the same thing as dividing the number by 100. Examples:[1]
    • 75% converts to .75
    • 3.1% converts to .031
    • 0.5% converts to 0.005
  2. Writing a number as a fraction of 100 is simply another way to write a percent. The number of the percent becomes the numerator of the fraction and 100 becomes the denominator. Simplify the fraction to its lowest form.[2]
    • Example: 36% turns to 36/100.
    • To simplify, look for the highest number that goes into 36 and 100. In this case, that would be 4.
    • Determine how many times 4 goes into 36 and 100. When you simplify, the answer would be 9/25.
    • To check that you’ve converted correctly, divide 9 by 25 (0.36) and multiply by 100 (36%). This number should equal your original percent.
    Advertisement
  3. Once the percent has been converted to a decimal or fraction, the % sign is no longer appropriate. Remember, percent just means per one hundred, so if you forget to remove the percent sign after converting, your answer will be off by one hundred.[3]
  4. Advertisement
Method 2
Method 2 of 3:

Converting Decimals

PDF download Download Article
  1. Another way of saying this is to move the decimal point two places to the right. A percent just means “per one hundred”, so the decimal becomes “per one hundred” after being multiplied. Don’t forget to add the percent sign after multiplying.[4] Examples include: 0.32 becomes 32%, 0.07 becomes 7%, 1.25 becomes 125%, 0.083 becomes 8.3%.
  2. A terminating decimal is one that does not repeat. Move the decimal point as many places to the right as you have decimals. This number is now the numerator of the fraction. The denominator is a 1 with as many zeros as you had decimals in the original number. Simplify the fraction at the end.[5]
    • For example: 0.32 has two decimal places. Move the decimal two places to the right and divide by 100: 32/100. With a common factor of 4, the fraction simplifies to 8/25.
    • Another example: 0.8 only has one decimal place. Move the decimal one place to the right and divide by 10: 8/10. With a common factor of 2, the fraction simplifies to 4/5.
    • To check your work, simply divide out the fraction and make sure it equals your original decimal: 8/25 = 0.32.
  3. Change a repeating decimal into a fraction. A repeating decimal is one that has a sequence of numbers that continually repeat. For example, if the number is 0.131313... there are 2 repeating decimals (13 is repeating). Determine how many repeating decimals there are and then multiply the decimal by 10n, where n is the number of repeating decimals.[6]
    • For example, 0.131313... is multiplied by 100 (10 to the power of 2) and we get 13.131313...
    • To determine the numerator (top number), subtract out the repeating portion of the decimal. For example, 13.131313... - 0.131313... = 13, so the numerator is 13.[7]
    • To determine the denominator (lower number), subtract 1 from the number you multiplied with. For example, 0.131313... was multiplied by 100, so the denominator is 100 - 1 = 99.
    • The final fraction for 0.131313… is 13/99
    • Additional Examples:
      • 0.333... becomes 3/9
      • 0.123123123... becomes 123/999
      • 0.142857142857... becomes 142857/999999
      • If necessary, take the fraction to the lowest term. For example, 142857/999999 becomes 1/7.
  4. Advertisement
Method 3
Method 3 of 3:

Converting Fractions

PDF download Download Article
  1. Divide the numerator by the denominator to change the fraction to a decimal. Interpret the fraction bar to mean "divided by". This means for any fraction x/y, it is the same as saying x divided by y.[8]
    • For example: The fraction 4/8 yields the decimal 0.5.
  2. Many numbers don’t divide evenly into each other. When you divide them, you have to decide how many decimal places you want to give in your answer. Oftentimes, the standard is two places. Remember the rules of rounding when truncating a fraction: if the next number is a 5, round the previous number up. For example, 0.145 rounds to 0.15.
    • For example: The fraction 5/17 yields the decimal 0.2941176470588…
    • The final decimal can be written simply as 0.29.
  3. Just as you did to convert the fraction to a decimal, divide the numerator by the denominator. Multiply the resulting decimal by 100 and add a percent sign to finish the conversion.[9]
    • If you had 4/8, dividing 4 by 8 would give you .50, then multiplying that number by 100 would give you 50. Adding a percent sign gives you your final answer by 50%.
    • Additional Examples:
      • 3/10 = 0.30 * 100 = 30%
      • 5/8= 0.625 * 100 = 62.5%
  4. Advertisement

Community Q&A

Search
Add New Question
  • Question
    How do I convert 27 over 56 into a fraction?
    Donagan
    Donagan
    Top Answerer
    "27 over 56" is already a fraction: 27/56.
  • Question
    What is 3 and 1 over 2 as a decimal?
    Donagan
    Donagan
    Top Answerer
    3½ = 3.5.
  • Question
    What is 62.5 as a fraction?
    Donagan
    Donagan
    Top Answerer
    62.5 (or the mixed number 62½) is the equivalent of the improper fraction 625/10, which reduces to 125/2. 125 ÷ 2 = 62.5.
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
Advertisement

Video

Tips

  • Knowing your times-tables will help you a lot.
  • Be warned that teachers can generally tell when a calculator has been used. If you are not supposed to use a calculator, it's probably best not to.
  • Many calculators have a fraction button. It may be possible to use the calculator to reduce the fraction to lowest terms. Check your instruction manual for details.
Submit a Tip
All tip submissions are carefully reviewed before being published
Name
Please provide your name and last initial
Thanks for submitting a tip for review!
Advertisement

Warnings

Advertisement

Things You'll Need

  • Paper and pencil
  • A standard calculator

You Might Also Like

Calculate PercentagesCalculate Percentages
Find the Greatest Common Divisor of Two IntegersFind the Greatest Common Divisor of Two Integers
Convert Radians to DegreesConvert Radians to Degrees
Convert Celsius (°C) to Fahrenheit (°F)°C to °F Conversion: A Complete Guide
Convert from Decimal to BinaryConvert from Decimal to Binary
Convert from Binary to DecimalConverting Binary to Decimal: Positional Notation & Doubling
Calculate Volume in LitresCalculate Volume in Litres
Convert a Number from Decimal to IEEE 754 Floating Point RepresentationConvert a Number from Decimal to IEEE 754 Floating Point Representation
Convert Milliliters (mL) to Grams (g)Convert Milliliters (mL) to Grams (g)
Convert Minutes to HoursConverting Minutes to Hours in Decimal or Hour & Minute Format
Convert from Decimal to HexadecimalConvert from Decimal to Hexadecimal: A Quick Guide + Examples
Convert Grams to KilogramsConversion Factor for Grams to Kilograms (and Kilograms to Grams)
Convert Pounds to KilogramsConvert Pounds to Kilograms with These Easy Tricks
Convert Kilometers to MilesConvert Kilometers to Miles
Advertisement

Expert Interview

Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with David Jia.

About This Article

David Jia
Co-authored by:
Math Tutor
This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 524,515 times.
1 votes - 100%
Co-authors: 98
Updated: March 22, 2024
Views: 524,515
Categories: Conversion Aids
Article SummaryX

The right way to convert percents, fractions, and decimals depends on what you're trying to convert them to. To convert a percent to a decimal, just move the decimal point 2 places to the left. To convert a fraction to a decimal, divide the numerator by the denominator. If you want to convert a decimal to a percent, multiply it by 100. If you want to make a percent a fraction, just put it over 100 and then simplify. To change a fraction to a percent, divide the fraction and then multiply it by 100. If you want to learn how to convert a repeating decimal into a fraction, keep reading the article!

Did this summary help you?

Thanks to all authors for creating a page that has been read 524,515 times.

Reader Success Stories

  • Shane Valerie Bautista

    Shane Valerie Bautista

    Jan 5, 2017

    "It helped me understand how to convert fractions, percent and decimals to scientific notation. What helped me the..." more
Share your story

Did this article help you?

Advertisement