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 0.35 to fraction:

0.35 = 35/100

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

gcd(35,100) = 5

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

0.35 = (35/5) / (100/5) = 7/20

Example #2

Convert 2.58 to fraction:

2.58 = 2+58/100

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

gcd(58,100) = 2

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

2+58/100 = 2 + (58/2) / (100/2) = 2+29/50

Example #3

Convert 0.126 to fraction:

0.126 = 126/1000

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

gcd(126,1000) = 2

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

0.126 = (126/2)/(1000/2) = 63/500

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...

100 x = 5.6565656...

100 x -  x = 99 x = 5.6

990 x = 56

x = 56/990 = 28/495

Decimal to fraction conversion table

DecimalFraction
0.0011/1000
0.011/100
0.11/10
0.111111111/9
0.1251/8
0.142857141/7
0.166666671/6
0.21/5
0.222222222/9
0.251/4
0.285714292/7
0.33/10
0.333333331/3
0.3753/8
0.42/5
0.428571433/7
0.444444444/9
0.51/2
0.555555555/9
0.571428584/7
0.6255/8
0.666666672/3
0.63/5
0.77/10
0.714285715/7
0.753/4
0.777777787/9
0.84/5
0.833333335/6
0.857142866/7
0.8757/8
0.888888898/9
0.99/10

 

 

Decimal to fraction converter ►

 


See also

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