Converting Fractions to Decimals: Tips and Tricks
Converting fractions to decimals is a key skill tested on the GRE and other standardized exams. Whether you’re brushing up on basic math concepts or aiming to increase your speed and accuracy, understanding this process can make a big difference on test day. In this guide, we’ll walk through how to convert fractions to decimals, including step-by-step examples and tips.
How to Convert Fractions to Decimals
A fraction represents part of a whole and is written with a numerator (the top number) and a denominator (the bottom number). A decimal is another way to express that value using base-10 notation.
The easiest way to convert a fraction to a decimal is by dividing the numerator by the denominator. For example, to convert the fraction ¾, divide 3 by 4. Using long division (4 into 3), you get 0.75. This method works for any fraction, but it can be time-consuming–especially on the GRE.
That’s why it’s helpful to memorize common fraction-to-decimal conversions ahead of test day. Doing so will save you time, reduce mental math, and improve your accuracy under pressure.
The table below lists some of the most frequently used tested conversions:
| Fraction | Decimal | Percent |
| 1/100 | .01 | 1% |
| 1/50 | .02 | 2% |
| 1/25 | .04 | 4% |
| 1/20 | .05 | 5% |
| 1/10 | .1 | 10% |
| 1/9 | .1111111… | 11.11% |
| 1/8 | .125 | 12.5% |
| 1/6 | .1666666…. | 16.67% |
| 1/5 | .2 | 20% |
| 1/4 | .25 | 25% |
| 1/3 | .3333333 | 33.33% |
| 2/5 | .4 | 40% |
| 1/2 | .5 | 50% |
| 3/5 | .6 | 60% |
| 2/3 | .6666666…. | 66.67% |
| 3/4 | .75 | 75% |
| 4/5 | .8 | 80% |
You should memorize the decimal conversions of common fractions like these. Note in the third column: if you want to convert the decimals to percentages, just move the decimal two places to the right.
Another method for converting fractions to decimals is to manipulate the fraction so that the denominator is 10 or 100 (or any power of 10). After all, percents are fractions of 100.
Here are a few simple examples:
Example 1
Convert ½ to a decimal by manipulating the denominator to a power of 10.
Conversion
Convert the fraction 1/2 to 5/10 by just multiplying by 5. Now it’s clear that 1/2 = .5
Example 2
Convert 13/20 to a decimal by manipulating the denominator to a power of 10.
Conversion
Remember, the goal is to convert the denominator to a power of 10. Multiply 20 by 5 to get 100, and convert the fraction to (5*13) / 100, or 65/100. As a result, 13/20 = .65
Example 3
Convert 18/30 to a decimal by manipulating the denominator to a power of 10.
Conversion
Same idea with 18/30. In this case, divide the denominator, 30, by 3 to get 10. Then, divide the numerator by 3 (18/3=6), and convert the fraction to 6/10, or .6
Example 4
Convert 9/15 to a decimal by manipulating the denominator to a power of 10.
Conversion
How about something tougher, like 9/15? Just because you can’t go from 15 to 100 in some multiplication, it doesn’t mean this strategy won’t work. I can first reduce 15 to 5, and then multiply that 5 by 2. To calculate, divide the numerator by 3, then multiply by 2.
So, 9/15 = 3/5 = 6 / 10 = .6
Example 5
Convert 11/40 to a decimal by manipulating the denominator to a power of 10.
Conversion
How about 11/40? Just divide by 2 then multiply by 5.
11/ 40 = 5.5 / 20 = 27.5 / 100 = .275
Ultimately, fractions are just shorthand for dividing. As long as the calculations are simple–in this case, 11/2 = 5.5, 5.5 * 5 = 27.5–then the strategy is advantageous.
Notice that this strategy will not work all the time. However, the GRE is unlikely to present you with difficult calculations; generally it will use numbers that are more manageable to work with.
Feel free to practice these in your head–that’s the idea. You don’t want to waste time configuring these calculations on paper. You want to save time and scratch paper space.
