Input the values of non-recurring part, recurring part, and the number in the repeating decimal to the 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.
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.
Following are the steps to convert repeating decimals into fractions.
Convert 0.123 into fraction form.
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.)