GRE Exam: A Simple Guide To Part-to-Whole Relationships - Decimals

A decimal is another way of representing a fraction, for example, , and so on.

Arithmetic with Decimals
Since the GRE provides you with a calculator, you should almost always use a calculator when adding and subtracting decimals.

The calculator will also come in handy when multiplying or dividing decimals, but as illustrated later, there are shortcuts you should be alert to when working with powers of 10.

Place Values
Every digit in a number has a place value. For example, in the number 237.98, 2 is in the hundreds place, 3 is in the tens place, 7 is in the units place, 9 is in the tenths place, and 8 is in the hundredths place.

Place Values and Powers of 10
Look at what happens when you multiply the preceding value by 10:

Note that the digits haven’t changed, but their place values have! This illustrates an important point: Whenever you multiply or divide a number by a power of 10, the decimal of the number shifts:

If you multiply a number by a positive power of 10, the decimal will move to the right as many places as the value of the exponent.

If you divide a number by a positive power of 10, the decimal will move to the left as many places as the value of the exponent:


SOLUTION: Move the decimal three places to the right in Quantity A: 2,798. Move the decimal two places to the left in Quantity B: 27.98. Quantity A is greater.

The process also works in reverse. If you are doing calculations with a number that has a lot of zeros to the right or to the left of the decimal, you can use powers of 10 as shorthand for those values:

Let’s look at a GRE-style example:

0.02
0.2
2
20
200

SOLUTION: To make the calculations easier, express the denominator as 1.9 × 105.

The fraction now reads:


SOLUTION: Divide numerator and denominator by 1.9 to arrive at:
. The correct answer is D.

Common-Fraction-Decimal-Percent Equivalencies