decimals fractions conversion converting

Converting Fractions to Decimals: Tips and Tricks

One quick way to convert a fraction to a decimal on the GRE is through the use of basic division. For example, using long division the fraction 3/4, (that’s 4 goes into 3, not vice versa), will yield .75. Luckily, there are simpler and faster ways to convert fractions to decimals. The most important method is, of course, memorizing common conversions.

FractionDecimalPercent
1/100.011%
1/50.022%
1/25.044%
1/20.055%
1/10.110%
1/9.1111111…11.11%
1/8.12512.5%
1/6.1666666….16.67%
1/5.220%
1/4.2525%
1/3.333333333.33%
2/5.440%
1/2.550%
3/5.660%
2/3.6666666….66.67%
3/4.7575%
4/5.880%

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.