Decimal to Fraction Calculator
This calculator converts a decimal number to a fraction.
How many decimal places repeat? If you are converting a repeating decimal to a fraction, enter the number of decimal places that repeat.
For a repeating decimal such as 2.33333.... you can enter 2.3 and Trailing decimal places to repeat = 1.
Convert a Decimal to a Fraction
- Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
- Remove the decimal places by multiplication: Count how many places are to the right of the decimal. If you have x decimal places then multiply numerator and denominator by 10x.
- Reduce the fraction: Find the Greatest Common Factor (GCF) of the numerator and denominator and reduce the fraction by dividing both numerator and denominator by the GCF.
- Simplify the remaining fraction to a mixed number fraction if possible.
Example: Convert 2.625 to a fraction
1. Rewrite the decimal number number as a fraction (over 1)
2. Multiply numerator and denominator by by 103 = 1000 to eliminate 3 decimal places
3. Find the Greatest Common Factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125
Decimal to Fraction
- For another example, convert 0.625 to a fraction.
- Multiply 0.625/1 by 1000/1000 to get 625/1000.
- Reducing we get 5/8.
Convert a Repeating Decimal to a Fraction
- Create an equation such that x equals the decimal number.
- Count the number of decimal places, y. Create a second equation multiplying both sides of the first equation by 10y.
- Subtract the second equation from the first equation.
- Solve for x
- Reduce the fraction.
Example: Convert repeating decimal 2.666 to a fraction
1. Create an equation such that x equals the decimal number
2. Count the number of decimal places, y. There are 3 digits in the repeating decimal group, so y = 3. Ceate a second equation by multiplying both sides of the first equation by 103 = 1000
3. Subtract equation (1) from equation (2)
4. Solve for x
5. Reduce the fraction. Find the Greatest Common Factor (GCF) of 2664 and 999 and reduce the fraction, dividing both numerator and denominator by GCF = 333
Repeating Decimal to Fraction
- For another example, convert repeating decimal 0.333 to a fraction.
- Create the first equation with x equal to the repeating decimal number:
x = 0.333
- There are 3 repeating decimals. Create the second equation by multiplying both sides of (1) by 103 = 1000:
1000X = 333.333 (2)
- Subtract equation (1) from (2) to get 999x = 333 and solve for x
- x = 333/999
- Reducing the fraction we get x = 1/3
- Answer: x = 0.333 = 1/3
To convert a fraction to a decimal see the Fraction to Decimal Calculator.
Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.
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