# Decimal to Fraction Conversion Calculator

Fraction result:
Calculation:

Fraction to decimal converter ►

#### Decimal to Fraction

This calculator converts a decimal number to a fraction or a decimal number to a mixed number. For repeating decimals enter how many decimal places in your decimal number repeat.

#### How to Convert a Decimal to a Fraction

1. Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).

2. Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Next, given that you have x decimal places, multiply numerator and denominator by 10x.

3. Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.

4. Simplify the remaining fraction to a mixed number fraction if possible.

#### Example:

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

#### Convert a Repeating Decimal to a Fraction

1. Create an equation such that x equals the decimal number.

2. Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10y.

3. Subtract the second equation from the first equation.

4. Solve for x

5. Reduce the fraction.

#### Example:

Convert 0.333333... to fraction:

x = 0.333333...

10x = 3.333333...

10x - x = 9x = 3

x = 3/9 = 1/3

Fraction to decimal conversion ►