Decimals
A decimal is another way of representing a fraction, for example,^14 = 0.25,^25 = 0.4,
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:
2 37. 9 8 × 10 = 2,379.8
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.
2.79 × 103 = 2,790
321.98 × 10 = 3,219.8
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:
3,293 ÷ 10^2 = 32.93
1,203.79 ÷ 10^3 = 1.20379
QUANTITY A QUANTITY B
2.7 98 × 103 2,798 ÷ 10^2 A B C D
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
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