0.7777777... = 0.7
1.85858585858585... = 1.85
253.207207207207207... = 253.207
3.610888888888... = 3.6108

The line drawn over the number(s) shows the repeating part of the decimal.

To convert repeating decimals to fractions, we want to multiply the decimal by a power of 10 such that subtracting the original number from it will cancel the repeating decimal part.
See the examples below to see how to convert repeating decimals to fractions.

Example 1: With only repeating numbers in the decimal

Convert the following decimals into simplified mixed fractions. If the whole number value of the fraction is 0, just leave it blank.

3.74

To make the problem easier, take out the whole number and just work on the decimal. In this problem, we will work on converting 0.74 into a fraction.

Let's assign x = 0.74747474...
The repeating part is 2 digits long so we multiply x by 10² or 100.
So now we have 100x = 74.74747474...

100x	=	74.	74747474...
-   x	=	0.	74747474...
99x	=	74
x	=	74 99

For the answer, we bring back the whole number.

3.74

=

Example 2: With non-repeating numbers in the decimal

Convert the following decimals into simplified mixed fractions. If the whole number value of the fraction is 0, just leave it blank.

2.0146

To make the problem easier, take out the whole number and just work on the decimal. In this problem, we will work on converting 0.0146 into a fraction.

Let's assign x = 0.0146464646...
The repeating part (46) is 2 digits long and the non-repeating part (01) is 2 digits long so we multiply x by 10⁽²⁺²⁾ or 10000.
So now we have 10000x = 146.46464646...

Since there is a non-repeating part in the decimal that is 2 digits long, we multiply x by 10² or 100.
Now we have 100x = 1.4646464646....

10000x	=	146.	46464646...
-   100x	=	1.	46464646...
9900x	=	145
x	=	145 9900
	=	29   1980

For the answer, we bring back the whole number.

2.0146

=