Decimal to Fraction Calculator


Quick conversion of any decimal to fraction.

The decimal-to-fraction calculator is just one of many tools available on Calcopolis for converting decimal numbers to fractions or mixed numbers. It can also help you in converting negative decimals or repeating decimals.

Decimals and fractions are two distinct representations of numbers less than one or between integers. They're both incredibly useful approaches for dealing with the calculations for these specific numbers.

Yet, in some cases, using fractions is more practical than using decimals. You see, a fraction clearly expresses the relationship between two integers in the form of a ratio. 

btw. You may be interested also in our ratio simplifier, which can turn complex ratios into simple and more readable versions representing the same mathematical proportion.

Whereas decimals can have the exact numerical value, they lack the clear demonstration that fractions have.

To clarify, assume we have a cake that's divided into 10 slices. If two slices were eaten, it would be easier to describe the remaining portion as  rather than 0.8, wouldn't it?

How to Convert Decimals to Fractions

There are two methods for converting decimals to fractions, depending on the type of decimal.

The first method is for converting rational decimal numbers, which are numbers that can be written as fractions. The second method is for converting repeating decimals, as well as irrational numbers, which are numbers that can't be expressed as fractions.

1st Method

Step 1: Create a Fraction

Simply create a fraction with the decimal 0.x as the numerator and the number 1 as the denominator to get a 

Step 2: Eliminate the Decimal Places

Count the number of decimal places to the right of the decimal point. The number you discovered y will be the power of the numerator and denominator in a fraction . Then, multiply this fraction by the initial fraction , which should remove the decimal places.

Step 3: Simplify the Fraction

The first step in simplifying a fraction is to determine if there's a number that can be divided by both the numerator and denominator. After you've identified the Greatest Common Factor (GCF), divide the numerator and denominator by it to get a much simpler fraction!

 Example: Convert 0.25 to a Fraction
  1. First, start by converting 0.25 to a fraction:
  2. Then, since there are two places after the decimal we'll multiply the fraction by :
  3. Finally, to simplify this fraction, multiply it by its GCF, which is 25:

2nd Method

Step 1: Make a Fraction

If you have a repeating decimal or an irrational number, identify the repeating digit and use it as the numerator of a fraction. The number 9 will be repeated with the number of repeated digits in the denominator of this fraction.

For instance, if the repeating decimal is 0.777...., the fraction will be . Because the number 7 is the only number that's repeated, there's only one 9. However, if you have 0.363636..., the fraction will be . Because there are two numbers 3 and 6, there'll be two 9s.

Step 2 (Optional): Add  Numbers to the Fraction

If the number to the left of the decimal point is greater than or equal to one, such as 1.838383..., it should be added to the fraction. In the end, remember to simplify the fraction you'll get, if possible.

 Example: Convert 1.6666 to a Fraction
  1. First, identify the repeating digit(s) to create a fraction accordingly:
  2. Then perform addition since the number to the left of the decimal point equals 1:

Alternatives

Instead of fractions, decimals may be presented as percentage values or ratios, depending on your needs. Percentages are sometimes more convenient, but people often make mistakes in percentage operations. 

If you wish to avoid them, use our percent calculator

In order to revert this operation, use our dedicated tool and reverse fractions to decimals


Authors

Created by Lucas Krysiak on 2022-12-21 16:53:53 | Last review by Mike Kozminsky on 2022-12-21 13:09:43

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