# Decimal to Fraction Converter

* You can enter decimals with e notation. e.g: 572 = 5.72e2.

Fraction to decimal converter ►

## How to convert decimal to fraction

#### Conversion stages

1. Write the decimal fraction as a fraction of the digits to the right of the decimal period (numerator) and a power of 10 (denominator).
2. Find the greatest common divisor (gcd) of the numerator and the denominator.
3. Reduce the fraction by dividing the numerator and the denominator with the gcd.

#### Example #1

Convert 0.32 to fraction:

0.32 =
32100

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(32,100) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

0.32 =
324
÷
1004
=
825

#### Example #2

Convert 2.56 to fraction:

2.56 = 2
56100

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(56,100) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

2
56100
= 2 +
564
÷
1004
= 2
1425

#### Example #3

Convert 0.124 to fraction:

0.124 =
1241000

Find the greatest common divisor (gcd) of the numerator and the denominator:

gcd(124,1000) = 4

Reduce the fraction by dividing the numerator and the denominator with the gcd:

0.124 =
1244
÷
10004
=
31250

## How to convert repeating decimal to fraction

#### Example #1

Convert 0.333333... to fraction:

x = 0.333333...

10x = 3.333333...

10x - x = 9x = 3

x =
39
=
13

#### Example #2

Convert 0.0565656... to fraction:

x = 0.0565656...

100x = 5.6565656...

100x - x = 99x = 5.6

990x = 56

x =
56990
=
28495

## Decimal to fraction conversion table

Decimal Fraction
0.00001 1/100000
0.0001 1/10000
0.001 1/1000
0.01 1/100
0.08333333 1/12
0.09090909 1/11
0.1 1/10
0.11111111 1/9
0.125 1/8
0.14285714 1/7
0.16666667 1/6
0.2 1/5
0.22222222 2/9
0.25 1/4
0.28571429 2/7
0.3 3/10
0.33333333 1/3
0.375 3/8
0.4 2/5
0.42857143 3/7
0.44444444 4/9
0.5 1/2
0.55555555 5/9
0.57142858 4/7
0.6 3/5
0.625 5/8
0.66666667 2/3
0.7 7/10
0.71428571 5/7
0.75 3/4
0.77777778 7/9
0.8 4/5
0.83333333 5/6
0.85714286 6/7
0.875 7/8
0.88888889 8/9
0.9 9/10
1.1 11/10
1.2 6/5
1.25 5/4
1.3 13/10
1.4 7/5
1.5 3/2
1.6 8/5
1.7 17/10
1.75 7/4
1.8 9/5
1.9 19/10
2.5 5/2

Fraction to decimal conversion ►