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Converting Between Decimals,
     Fractions, and Percents (page 2 of 3)

Decimal to Percent

Decimal-to-percent conversions are simple: just move the decimal point two places to the right. (Remember, $0.50 is one-half, or 50%, of a dollar.) For example:

0.23 = 23%
2.34 = 234%
0.0097 = 0.97%

(Note that 0.97% is less than one percent. It should not be confused with 97%, which is 0.97 as a decimal.)

Fraction to Decimal

If you remember that fractions are division, then this is easy. The calculator can do the work for you, because you can just have it do the division. For example:

The bar is placed over the repeating digits, for convenience sake.

When converting fractions to decimals, you may be told to round to a certain place or to a certain number of decimal places. For instance, looking at that last example, ²/₇ as a decimal rounded to the nearest tenth (rounded to one decimal place) is 0.3; to the nearest hundredth (to two decimal places) is 0.29; to the nearest thousandths (to three decimal places) is 0.286; to the nearest ten-thousandths (to four decimal places) is 0.2857; et cetera. If you're not sure how you should format your answer, then give the "exact" form and the rounded form:

Note that the rounded form can be useful for word problems, where a final answer in rounded form may be more practical than a repeating decimal.

Fraction to Percent

This conversion starts the same as the previous one, but the final answer can come in a couple different formats sometimes. You always start by doing the division (fractions are division, remember!), and then (usually) you move the decimal point two places to the right. For example:

However, sometimes the "decimal expansion" doesn't end. This is where the answer can come in a couple different formats. You can either round the answer, or use a fraction inside the percent. For instance:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

You can round this to, say, 0.389 = 38.9%. But if you aren't supposed to round, put out a sheet of paper and do the long division. You'll need to get TWO decimal places of answer across the top, and then look at the remainder at the bottom:

Fractions are division, so I took the 7and divided by the 18. I kept going until I had TWO decimal places (the ".38") across the top. At that point, the remainder is 16. If you think back to elementary school, you handle the remainder by putting it over the divisor (18, in this case), and tacking it on to the number across the top. In this case, I get:

So ⁷/₁₈, expressed as an unrounded decimal, is 38 ⁸/₉%. This probably looks a little weird, so let's do a couple more examples. For instance, other than memorizing, how are you supposed to know that 0.333333... = ¹/₃? Here's how:

This doesn't end, so do the long division by hand:

Note that the remainder is 1 and the divisor is 3, so you'll be tacking a " ¹/₃ " on to the "0.33" from the top:

Here's a messier example that you won't have memorized:

This doesn't end, so do the long division by hand:

Note that the remainder is 10 and the divisor is 35, so you'll be tacking a " ¹⁰/₃₅ " on to the "0.54" from the top:

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