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.
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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.
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.
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.
