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.

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About the Author

Jon Zamboni began writing professionally in 2010. He has previously written for The Spiritual Herald, an urban health care and religious issues newspaper based in New York City, and online music magazine eBurban. Zamboni has a Bachelor of Arts in religious studies from Wesleyan University.

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