Sunday, 13 September 2015

Decimal to Fraction Conversion

Enter a decimal number and press the Convert button:

Example: convert 2.56 to fraction:

2.56 = 2+56/100

gcd(56,100) = 4

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

Count the number of digits (d) to the right of the decimal point of the decimal number x.Example: 2.56 has 2 digits to the right of the decimal point, so d=2.
Calculate the factor (f) for making the decimal number an integer:
f = 10^d
Example:

f = 10² = 100
Multiply and divide the decimal number x by the factor f:
x × f / f = y / f
Example:

2.56 × 100 / 100 = 256 / 100

gcd(256,100) = 4

Reduce the fraction by dividing the numerator and denominator by the gcd value:Example:

256 / 100 = (256/4) / (100/4) = 64/25

Convert 0.333333... to fraction:

x = 0.333333...

10x = 3.333333...

10x - x = 9x = 3

x = 3/9 = 1/3

Convert 0.0565656... to fraction:

x = 0.0565656...

100x = 5.6565656...

100x - x = 99x = 5.6

990x = 56

x = 56/990 = 28/495