Math Help: Converting Fractions to Decimals

In middle school, many students learn to convert proper and improper fractions to decimals. Keep reading for instructions on how to perform this important math operation!

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Turning Fractions into Decimals

Every fraction has an equivalent decimal. To find out what it is, you'll need to divide the fraction's numerator (top number) by its denominator (bottom number). If you're converting an improper fraction, where the numerator is larger than the denominator, you can use standard division. For instance, 10/2 = 5.

If the numbers are large or if the answer has a remainder, you'll need to use your long division skills. Here's a step-by-step example of converting a fraction to a decimal when there's a remainder:

  1. Remember that in long division, the dividend - the number you're dividing into - goes on the inside of the long division bracket, and the divisor - the number you're dividing by - goes on the outside. For example, if your fraction is 15/6, the number 15 goes on the inside and six goes on the outside.
  2. Now, follow standard long division procedures. You'll end up with a 2 on the long division line above the 5, since 6 goes into 15 twice. Since 2 x 6 = 12 and 15 - 12 = 3, you'll need to bring down a zero beside the 3 to make it 30. Then, divide 30 by 6.
  3. Since 30 ÷ 6 = 5, you'll place a decimal point beside the 2, followed by a 5. Since 5 x 6 = 30 and 30 - 30 = 0, your final answer is 2.5.

Converting Proper Fractions

If you're converting a regular fraction, like 4/5, then you'll have to use long division to divide a smaller number by a larger one. Here are the steps that you'll follow to convert 4/5 into a decimal:

  1. The dividend is 4, so it will go on the inside of the long division sign. The divisor, 5, goes on the outside.
  2. Since 5 doesn't goes into 4, place a 0 above the 4 on the long division line, and then place a decimal point to the right of the 0. Next, multiply 0 by 5 and write the answer below the 4. Since 0 x 5 = 0, write 0.
  3. Since 4 - 0 = 4, and we've already determined that 5 can't go into 4, you'll have to add a 0 to the dividend and bring it down to make the 4 into 40. Now, 5 goes into 40 exactly 8 times, so place an 8 above the 0 in 40 and to the right of the decimal point above the division line. Since 8 x 5 = 40 and 40 - 40 = 0, the final answer to this division problem is 0.8.

Repeating Decimals

When you convert some fractions into decimals using the procedures explained above, you'll find that they don't stop after one or two decimal places. They may continue for many decimal places, and they may even repeat infinitely. For decimals that repeat infinitely, you can indicate this by putting a small horizontal line over the digit to the right of the decimal point. For decimals that seem very long, but don't display any obvious pattern, you should check your work. If you find that you've performed all of your calculations correctly, you may need to simply round off your decimal.

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