Converting a Decimal to a Fraction, and a Fraction to a Decimal

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Converting Fractions to Decimals

Converting fractions to decimals is much easier than doing the opposite. After all, a fraction is just one number divided by another, right? If you actually divide the numerator by the denominator, the result will be a decimal. You can do the division by hand or with a calculator – either will get you the correct answer.

For example, look at the fraction ¾. How can you convert it to a decimal? Divide 3 by 4. If you do it on a calculator, you’ll get the answer right away: .75. If you do it by hand, it won’t take you much longer. Try it.

Note: There are some fractions that turn into repeating decimals when you divide their numerators by their denominators. For example, try converting 2/3 into a decimal. Whether you do it by hand or with a calculator, the result will be .6666666…. It will never stop! We write these results as decimals with a line over the repeating number. For example, you would write the above repeating decimals as .6 with a line over the six.

Converting Decimals to Fractions

It’s easy to convert a decimal to a fraction, assuming that you know how to read a decimal correctly. For example, you would read the decimal .2 as “two tenths” – which is actually a fraction! So .2 = 2/10. You would read the decimal .25 as “twenty-five hundredths,” so .25 = 25/100.

What if you’re not sure how to read a decimal correctly? What if you’d read the two decimals above as “point two” or “point two five”? If so, just follow this rule. Count how many digits are after the decimal point. When you write your fraction, put a one and that many zeros in the denominator. For example, look again at .25. There are two digits after the decimal point – 2 and 5. Therefore, you would know that the decimal has two zeros, so it would be 100.

One last point – don’t leave the fraction as 25/100 or 2/10. Reduce it! For example, .25 = 25/100 = ¼.

Note: What if there are digits before the decimal point? Make sure to keep them out of the fraction. The digits before the decimal point represent a whole number, so they should stay in front of the fraction as part of a mixed fraction. For example, 34.2 would convert to 34 2/10 or 34 1/5.

This post is part of the series: Fraction, Decimal, and Percent Conversions

Confused about how to do fraction, decimal, and percent conversions? It can get complicated, but if you learn each conversion separately, you’ll soon be converting like a pro!

  1. Converting Decimals to Percents and Percents to Decimals
  2. Converting Fractions to Decimals and Decimals to Fractions
  3. Converting Percents to Fractions and Fractions to Percents