Decimal to Fraction Calculator

With the convenience of the decimal to fraction calculator aside, let’s not forget the importance of being able to manually convert decimal to fraction on paper.

Terminating decimals have a limited number of digits after the decimal point. Follow these steps to manually convert any terminating decimal into a fraction:

Step a: Write the decimal number in fraction format, with the number as the numerator and 1 in the denominator.

Step b: Now, multiply the numerator and the denominator by 10 for every digit left of the decimal point.

Step c: Next, reduce the fraction into its simplest form.

Terminating Decimal to Fraction Example: 6869.22 = 6869 ²²/₁₀₀

Non-terminating also known as recurring decimals are those decimals which have one or more repeating digits after the decimal point which continue on infinitely. Non-terminating decimals are typically more complex to manually convert into fractions. Next we'll explain the steps involved.

Let us find the value of decimal 0.4444... in fraction form.

Step 1: Take the repeating decimal you are trying to convert as x. Let x be equal to 0.44444….

Step 2: Multiply the value of X by the power of 10, such that the resulting number has the same number on the right side of the decimal.

Hence, 10x = 4.44444….

Step 3: Subtact the output of the the first two steps

10x-x = 4.444444...-0.4444444….

9x= 4

= 4/9

Step 4: Resulting in a fraction number of the decimal number.

x=4/9

Recurring Decimal to Fraction Example:

Irrational decimals go on forever and never form a repeating pattern. This type of decimal cannot be expressed as a fraction.

Irrational Decimal Example: 0.958044949.....