To convert a decimal to a fraction, write the decimal over the correct power of 10 and reduce the result. The number of decimal places tells you whether the denominator starts as 10, 100, 1,000, or another power of 10. These three steps show how to turn any terminating decimal into a fraction in simplest form.
Already have a number to convert? Use the Decimal to Fraction Calculator for an exact answer and calculation steps.
Count the digits to the right of the decimal point. One decimal place uses 10 as the denominator, two places use 100, and three places use 1,000. This identifies the power of 10 needed to write the decimal as a fraction.
Remove the decimal point and place the resulting integer over that power of 10. Keep a negative sign if the original decimal is negative. For a decimal greater than 1, this step may create an improper fraction.
Find the greatest common divisor of the numerator and denominator. Divide both by that number to simplify the decimal fraction. If the result is an improper fraction, you can also write it as a mixed number.
Step 1: 0.625 has three decimal places, so the denominator is 1,000.
Step 2: 0.625 = 625/1000.
Step 3: The greatest common divisor of 625 and 1,000 is 125. Divide the numerator and denominator by 125:
625/1000 = 5/8
Final Answer: 0.625 = 5/8.
Step 1: 2.75 has two decimal places, so the denominator is 100.
Step 2: 2.75 = 275/100.
Step 3: The greatest common divisor of 275 and 100 is 25:
275/100 = 11/4
The improper fraction 11/4 can also be written as the mixed number 2 3/4. Both forms have the same value. Try more values with the decimal to mixed number calculator.
Final Answer: 2.75 = 11/4 = 2 3/4.
Step 1: -0.5 has one decimal place, so the denominator is 10.
Step 2: Keep the negative sign: -0.5 = -5/10.
Step 3: The greatest common divisor of 5 and 10 is 5:
-5/10 = -1/2
Final Answer: -0.5 = -1/2.
A repeating decimal needs an algebraic step because its digits do not end. For 0.333..., let x = 0.333.... Multiplying by 10 gives 10x = 3.333.... Subtract the first equation from the second: 9x = 3, so x = 1/3.
The same method works for 0.666.... Let x = 0.666..., so 10x = 6.666.... Subtraction gives 9x = 6, and dividing by 9 gives x = 6/9 = 2/3. The calculator accepts finite decimal input; it does not accept repeating-bar or infinite notation.
Use the same place-value method for a decimal greater than 1. The value 2.75 becomes 275/100, which simplifies to the improper fraction 11/4. Dividing 11 by 4 gives a quotient of 2 and a remainder of 3, so the equivalent mixed number is 2 3/4.
The improper fraction and mixed number are both exact. Use the decimal to mixed number calculator when you want both forms and their calculation steps.
| Decimal places | Starting denominator | Example |
|---|---|---|
| 1 decimal place | 10 | 0.5 = 5/10 |
| 2 decimal places | 100 | 0.25 = 25/100 |
| 3 decimal places | 1,000 | 0.625 = 625/1000 |
| 4 decimal places | 10,000 | 0.0625 = 625/10000 |
Wrong: 0.75 = 75/100
Correct: 0.75 = 3/4
The first fraction has the right value, but it is not in simplest form. Divide both numbers by their greatest common divisor.
Wrong: 0.625 = 625/100
Correct: 0.625 = 625/1000
There are three decimal places in 0.625, so the starting denominator must be 1,000.
Wrong: 2.75 = 3/4
Correct: 2.75 = 11/4 = 2 3/4
When you convert a decimal greater than 1 to a fraction, the whole-number value must remain part of the answer.
For a repeating decimal such as 0.333..., set x equal to the decimal, multiply by a power of 10 that moves the repeating block, subtract the two equations, and solve for x. For example, 0.333... = 1/3. A repeating decimal always has a fraction equivalent because the repeating part cancels out in the subtraction step.
A terminating decimal has a finite number of digits after the decimal point, such as 0.625 or 2.75. Terminating decimals are converted by writing the digits over a power of 10 and simplifying, as shown in the three steps above.
Use the same three steps. 2.75 becomes 275/100, which simplifies to 11/4, an improper fraction. You can also write it as the mixed number 2 3/4. Both forms are correct — see decimal to mixed number conversion for more examples.
Simplest form is the standard way to report a fraction. 75/100 and 3/4 have the same value, but 3/4 is the simplified answer. To simplify, divide the numerator and denominator by their greatest common divisor.
