# GRE Arithmetic - Fraction, decimal conversions

If you need to convert a fraction to a decimal, simply divide the denominator of the fraction into the numerator. If both the numerator and denominator are even, then you'll be able to convert the fraction into a non-repeating number. Otherwise you cannot fully divide the denominator into the numerator, and you have to realize that the resulting decimal number is a **repeating decimal**. For example, assume that in the midst of answering a GRE math question, you need to answer the following:

What is the decimal value of three divided by four, 3/4?

Okay, that's not too bad. Simply divide three by four, to get 0.75. It might take you a second or two to do the calculation (or, better yet, you've had ample practice so that you KNOW that 3/4 is 0.75), but regardless it's not rocket science!

A bit more challenging is the following:

What is the decimal value of three divided by seventeen, 3/17?

Hmm. A bit more difficult. If you do the calculation, you'll get 0.1764705, etc., which is a non-repeating decimal. Which, can be rounded to 0.18. Again, such tedious calculations you don't need to do out-right on the GRE test, but you might need to do such quick math while working towards the solution of one of the harder math questions.

To change a decimal into a fraction, the numbers to the right of the decimal place make up the numerator of the resulting fraction. Count the number of decimal places to the right of the decimal place. If there are two decimal places to the right of the decimal place, then create the fraction by placing the numbers to the right of the decimal place over 100. If there are three decimal places to the right of the decimal place, create the fraction by placing the numbers to the right of the decimal place over 1000.