How to Change a Decimal to a Fraction


Fractions and decimals represent the same thing: a part of a whole. For example, 0.25 and 1/4 both mean one-quarter or 25 percent. Converting some decimals -- such as those with more than two numbers after the decimal point -- to fractions makes it easier to visualize them. You can convert decimals to fractions quickly, using basic multiplication and division.

Converting Decimals to Fractions

  • Write the decimal number above the number 1, as if you are going to divide it. For example, if the decimal is 0.625, write 0.625/1. Multiply both 0.625 and 1 by the multiple of 10 with the same amount of zeros as there are numbers after the decimal point. Since 0.625 has three numbers after the decimal point, multiply the numbers by 1,000, for example:

    0.625 X 1,000 = 625
    1 X 1,000 = 1,000

    The top number is now a whole number, 625, and the 1 is now 1,000, yielding the fraction 625/1,000.

Simplifying Fractions

  • The number 625/1,000 is a decimal fraction, meaning that you can reduce it to a smaller fraction. Do this by dividing both the top and bottom number by a common divisor, which is a number that both numbers can be evenly divided by. Both of these numbers can be divided equally by 25, so use that number to reduce the fraction. The equations would be: 625/25 = 25 and 1,000/25 = 40. Write this as a fraction: 25/40. This fraction can be reduced once more. Both 25 and 40 are divisible by 5, so use 5 to reduce as follows: 25/5 = 5 and 40/5 = 8, yielding the fraction 5/8. Since 5/8 is a common fraction, meaning it cannot be reduced, this is your final answer.


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