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Converting Between Decimals,
     Fractions, and Percents (page 1 of 4)

Sections: Percent to Decimal, Percent to Fraction, Decimal to Fraction, Decimal to Percent,
               Fraction to Decimal, Fraction to Percent, Tables of Equivalents

Percentages refer to fractions of a whole; that is, whatever you're looking at, the percentage is how much of the whole thing you have. For instance, "50%" means " ¹/₂ "; "25%" means " ¹/₄ "; "40%" means " ²/₅ "; et cetera.

Often you will need to figure out what percentage of something another thing is. For instance, if a class has 26 students, and 14 are female, what percentage of the students are female?  It is 14 out of 26, or ¹⁴/₂₆ = 0.538461538462..., or about 54%. (For more information on percent word problems, look at the Percent of lesson.)

"Percent" is actually "per cent", meaning "out of a hundred". (It comes from the Latin per centum for "thoroughly hundred".) You can use this "out of a hundred" meaning, along with the fact that fractions indicate division, to convert between fractions, percents, and decimals.

Percent to Decimal

Percent-to-decimal conversions are easy; you mostly just move the decimal point two places. The way I keep it straight is to remember that 50%, or one-half, of a dollar is $0.50. In other words, you have to move the decimal point two places to the left when you convert from a percent (50%) to a decimal (0.50). Some more examples are:

27% = 0.27
104% = 1.04
0.5% = 0.005

You can use the Mathway widget below to practice "Ratios, Proportions, and Percents", subtopic "Converting Percents to Decimal". Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free seven-day trial of the software.)

Percent to Fraction

Percent-to-fraction conversions aren't too bad. This is where you use the fact that "percent" means "out of a hundred". Convert the percent to a decimal, and then to a fraction. For instance:

Now you can reduce the fraction:   Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved

Most conversions are simple like this, but some require a little extra care. The reason I converted to a decimal first is that the number of decimal places tells me how many zeroes to have underneath. Notice that "0.40" can also be written as "0.4". Then 0.4 = ⁴/₁₀  =  ²/₅, which is the same answer as before. It works out because "0.4" has one decimal place and "10" has one zero. This concept (matching the number of decimal places with the number of zeroes) helps in more complicated problems:

Another example:

If you have a graphing calculator, you can probably have the calculator do this conversion for you. Check your manual.

You can use the Mathway widget below to practice "Ratios, Proportions, and Percents", subtopic "Converting Percents to Fractions". Try the entered exercise, or type in your own exercise. Then click "Answer" to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)

(Clicking on "View Steps" on the widget's answer screen will take you to the Mathway site, where you can register for a free seven-day trial of the software.)

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