Decimal to Fraction Calculator

How to Convert a Negative Decimal to a Fraction

1. Remove the negative sign from the decimal number
2. Perform the conversion on the positive value
3. Apply the negative sign to the fraction answer

If a = b then it is true that -a = -b.

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 10^x.
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 2.625 to a fraction

1. Rewrite the decimal number number as a fraction (over 1)
   2.625 = 2.625/1
2. Multiply numerator and denominator by by 10³ = 1000 to eliminate 3 decimal places
   2.625/1 × 1000/1000 = 2625/1000
3. Find the Greatest Common Factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125
   2625÷125/1000÷125 = 21/8
4. Simplify the improper fraction
   = 2 5/8

Therefore, 2.625 = 2 5/8

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

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 10^y.
3. Subtract the second equation from the first equation.
4. Solve for x
5. Reduce the fraction.

Example: Convert repeating decimal 2.666 to a fraction

1. Create an equation such that x equals the decimal number
   Equation 1: x = 2.666...
2. Count the number of decimal places, y. There are 3 digits in the repeating decimal group, so y = 3. Create a second equation by multiplying both sides of the first equation by 10³ = 1000
   Equation 2: 1000x = 2666.666...
3. Subtract equation (1) from equation (2)
   1000x - x = 2666.666... - 2.666...
   999x = 2664
4. Solve for x
   x = 2664/999
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
   2664÷333/999÷333 = 8/3
6. Simplify the improper fraction
   = 2 2/3

Therefore, 2.666... = 2 2/3

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