# 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 = 32/100

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 = (32/4) / (100/4) = 8/25

#### Example #2

Convert 2.56 to fraction:

2.56 = 2+56/100

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+56/100 = 2 + (56/4) / (100/4) = 2+14/25

#### Example #3

Convert 0.124 to fraction:

0.124 = 124/1000

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 = (124/4) / (1000/4) = 31/250

## 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 = 3/9 = 1/3

#### Example #2

Convert 0.0565656... to fraction:

x = 0.0565656...

100x = 5.6565656...

100x - x = 99x = 5.6

990x = 56

x = 56/990 = 28/495

## Decimal to fraction conversion table

Decimal Fraction
0.001 1/1000
0.01 1/100
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
0.625 5/8
0.66666667 2/3
0.6 3/5
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

Decimal to fraction converter »

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