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Repeating decimal to fraction calculator

Input the values of non-recurring part, recurring part, and the number in the repeating decimal to the fraction calculator.

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Repeating decimal to fraction calculator

The repeating decimal to fraction calculator is used to convert the recurring decimal values into over or fraction form. It can be used multiple times for free.

To convert fractions back into decimals, use the fraction to decimal calculator.

What is a repeating decimal?

A repeating decimal means the digit or the group of digits that repeats itself consecutively after the decimal point in a value.

It is represented by a bar symbol on top e.g 34 in.

How to convert recurring decimals into fractions?

Following are the steps to convert repeating decimals into fractions.

  1. Assign a variable to the digit.
  2. Remove the bar and expand the number. Call it equation 1.
  3. Multiply with the power of ten equal to the number of digits repeating, on both sides. Call it equation 2.
  4. Subtract equation 1 from 2.
  5. Take the numerical constant of the variable in the division on the right-hand side.
  6. Divide the values with the GCF.

Example:

Convert 0.123 into fraction form.

Example:

Step 1: Assign a variable and expand the number.

y = 0.123

y = 0.123123123… (equation i)

Step 2: Multiply with 1000 on both sides as there are 3 repeating digits.

y x 1000 = 0.123123123… x 1000

1000y = 123.123123… (equation ii)

Step 3: Subtract equation (i) from equation (ii).

1000y - y = 123.123123… - 0.123123…

999y = 123

y = 123 / 999

Step 4: Divide numerator and denominator with GCF.

The greatest common factor is 3.

y = 41 / 333

(Note: If the fraction is improper convert it into a proper fraction.)