One particularly tricky type of question in the GRE quant section is a question involving a terminating decimal. Don’t worry: help is at hand!

Consider the following question from the official GRE guide:

If 1 / [(211) x (517)] is expressed as a terminating decimal, how many nonzero digits will the decimal have?

A) One
B) Two
C) Four
D) Six
E) Eleven

Step 1: Know what a terminating decimal is

The first thing to consider is: what is a terminating decimal? A terminating decimal, true to its name, is a decimal that has an end. 

For example, 1 / 4 can be expressed as a terminating decimal: It is 0.25. 

In contrast, 1 / 3 cannot be expressed as a terminating decimal, because it is a recurring decimal, one that goes on forever. In other words, as a decimal 1/3 is 0.33333….. And those threes go on forever. 

Step 2: Simplify the expression

Start by considering only the denominator, which is (211) x (517). 

On all questions involving exponents, try to work with either the same bases or the same exponents. For example, 517 can be represented as 511 x 56.

Thus, (211) x (517) becomes 211 x 511 x 56, which then becomes 1011 x 56.

Now, this is all in a denominator with a numerator of 1. We can calculate 1/1011 as 0.00000000001. 

56 can be worked out on the calculator supplied on the GRE to be 15625.

Using the calculator, we get the reciprocal to be 1/15625 = 0.000064.

Multiplying 0.000064 by 1 / 1011 (or 0.00000000001) will not change the number of non-zero digits. Thus, our answer is B) Two.

The key to answering such questions quickly is firstly to understand the terminology. The second key point is to simplify the expression by making the bases or exponents the same. If you follow these steps, you will be able to solve even seemingly difficult questions quickly.