# How to Convert Decimals to Fractions for Math Problems

By Sandy Fleming
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Decimals and fractions both represent portions of the whole. In fact, every decimal has a matching fraction name and every fraction has a matching decimal name. When decimal numbers are read correctly, the fraction name becomes very clear. Read ".5" as "five tenths" and ".02" as "two hundredths," for example. Resist the urge to read those numbers as "point five" and "point zero two" because those names are not only incorrect, they obscure the connection between decimals and fractions.

Read the decimal correctly, using the place value name. To do this, read the number to the right of the decimal point as if it were a whole number. Add the name of the final place after you have said the number. The names of the places to the right of the decimal point mirror the names of the places of whole numbers. They are tenths, hundredths, thousandths, ten thousandths, and so on. For example, read ".15" as "fifteen hundredths" because the digits "1" and "5" together are read as "fifteen" and the number takes up two places to the right of the decimal point: the tenths and the hundredths. ".157" would be read as "one hundred fifty-seven thousandths" by the same logic.

Consider the place value name that applies to the decimal you have read. That is the bottom number, or denominator, of your fraction. The top number, or numerator, is the actual number to the right of the decimal place. For the decimal ".25," place the "25" on the top of the fraction bar. Put a "100" on the bottom of the fraction since the decimal would be read as "twenty-five hundredths."

Simplify the fraction you have created if necessary. To put a fraction in simplest form, or lowest terms, divide numerator and denominator by the largest number possible, otherwise known as the greatest common factor. Both top and bottom numbers must be divided by the same number to simplify the fraction. In our example of "twenty-five hundredths," both 25 and 100 can be divided by 25. When that is done, the fraction in lowest terms is seen to be one-fourth.

Fractions can also be simplified by using multiple divisions instead of a single division by the greatest common factor. For the example fraction of 25/100, both numbers are divisible by five. Performing this operation would yield 5/20. Both of those numbers are also divisible by five. The answer to that calculation is 1/4. It is important to continue divisions in this manner until the numerator and denominator can no longer be divided by the same number.