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Unformatted text preview: = ⎯ = 0.05
0.09
0.0900
900
100 * Manhattan GMAT Prep
the new standard 19 Chapter 1 DIGITS & DECIMALS STRATEGY
POWERS AND ROOTS
To square or cube a decimal, you can always simply multiply it by itself once or twice.
However, to raise a decimal to a larger power, you can rewrite the decimal as the product of
an integer and a power of ten, and then apply the exponent.
(0.5)4 = ?
Rewrite the decimal:
Apply the exponent to each part: Take a power or a root of
a decimal by splitting the
decimal into 2 parts: an
integer and a power of
ten. 0.5 = 5 × 10 −1
(5 × 10−1)4 = 54 × 10−4 Compute the first part and combine: 54 = 252 = 625
625 × 10−4 = 0.0625
Solve for roots of decimals the same way. Recall that a root is a number raised to a fractional power: a square root is a number raised to the 1/2 power, a cube root is a number raised
to the 1/3 power, etc.
3 0.000027 = ? Rewrite the decimal. Make the first number something you can take the cube root of easily:
0.000027 = 27 ×10 −6 Write the root as a fractional exponent: (0.000027)1/3 = (27 × 10 −6)1/3 Apply the exponent to each part: (27)1/3 × (10−6)1/3 = (27)1/3 × 10−2 Compute the first part and combine: (27)1/3 = 3
(since 33 = 27)
−2
3 × 10 = 0.03 Powers and roots: Rewrite the decimal using powers of ten!
Once you understand the principles, you can take a shortcut by counting decimal places.
For instance, the number of decimal places in the result of a cubed decimal is 3 times the
number of decimal places in the original decimal:
(0.04)3 = 0.000064 (0.04)3
2 places = 0.000064
2 × 3 = 6 places Likewise, the number of decimal places in a cube root is 1/3 the number of decimal places
in the original decimal:
3 0.000000008 = 0.002 3 0.000000008
9 places = 0.002
9 ÷ 3 = 3 places However, make sure that you can work with powers of ten using exponent rules. Manhattan GMAT Prep
* 20 the new standard IN ACTION DIGITS & DECIMALS PROBLEM SET Chapter 1 Problem Set
Solve each problem, applying the concepts...
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 Spring '07
 MEJIAS

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