How to Convert Fractions to Decimals

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Converting fractions to decimals is just another way of expressing division. The same tools you use to divide whole numbers help you turn a fraction into a decimal. In addition, you can use a few shortcuts to make the process simpler to understand.

Numerators, Denominators and Division

  • To convert a fraction into a decimal, you must understand numerators and denominators. The numerator is the top number in a fraction, and the denominator is the bottom number. For example, in the fraction 3/5, the numerator is 3, and the denominator 5.

    However, a fraction is also an expression of division. The value of a fraction is equal to the numerator divided by the denominator. So 3/5 is equal to 3 divided by 5, or 0.6. You can thus convert a fraction into a decimal by using either long division or a calculator.

Power of 10 Shortcut

  • You can take advantage of a fraction's properties to solve fractions by hand. For example, when you multiply the denominator of a fraction by a number, you also multiply the numerator by that same number. This lets you easily convert fractions to decimals if you can turn the denominator into a power of 10 -- such as 10, 100 or 1,000.

    Take 3/5 again. You can multiply both the numerator and denominator by 2 to produce a denominator of 10. This gets you the fraction 6/10. Remember that a fraction is just division of the numerator by the denominator. When you divide a number by a power of 10, you move the decimal point one place to the left for each zero. So 6/10 is 0.6, 6/100 is 0.06, and 6/1,000 is 0.006. You get the same result for 3/5, only doing multiplication instead of long division.

Improper and Mixed Fractions

  • You can use the same power-of-10 technique for improper and mixed fractions, which are fractions larger than 1. An improper fraction, such as 7/4, has a numerator that's higher than the denominator. To convert this fraction into a decimal, use the same trick by multiplying to get a power of 10. Multiplying both the numerator and the denominator by 25 will produce the fraction 175/100, which you can divide. Remember that you move the decimal point one to the left for each zero in the denominator, so 7/4 = 175/100 = 1.75.

    A mixed fraction, such as 3 6/25, is a different way of expressing an improper fraction. To convert a mixed fraction to a decimal, set aside the number outside the fraction and do decimal conversion for the fraction. You add the number outside the fraction to your decimal afterward. For 3 6/25, set aside the 3, then convert the fraction by multiplying both the numerator and denominator by 4, getting 24/100, or 0.24. Then add 0.24 to 3, getting 3.24. So 3 6/25 = 3.24.

Repeating Decimal Numbers

  • If you are doing long division to convert a fraction into a decimal, you may run into a situation where you continue dividing forever. When you divide 1 by 3, it produces an endless decimal:

    0.3333333333...

    This is called a repeating decimal, designated by either an ellipsis (...) at its end or a bar called a vinculum that is placed over the repeating digits. If you encounter a repeating decimal, you can stop doing division and place a note that the decimal repeats using ellipsis or a bar. A repeating decimal may not be limited to a single repeating digit. For example:

    5/6 = 0.83333...
    1/7 = 0.142857142857...

    For 5/6, the ellipsis designates only that the digit 3 is repeating. The vinculum would be placed over the 3 only. For 1/7, the 142857 repeats endlessly.

References

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