What is the decimal equivalent of (1/5)^2 ?

Question

What is the decimal equivalent of  (\frac{1}{5})^5  ?

A) 0.00032

B) 0.0016

C) 0.00625

D) 0.008

E) 0.03125

Bunuel · Accepted Answer

(\frac{1}{5})^5=(\frac{2}{10})^5=(\frac{32}{10^5})=0.00032 .

Answer: A.

akadiyan · Answer

Decimal equivalent of  (1/5)^5 ?

Since we need decimal equivalent , we can start by converting value 1/5 to decimal. 1/5 is 0.20.

We need to find the value of  (0.2)^5  , we know the value of  2^5  = 32 , so we should look for the value of 32 in the answer choice and include the necessary 0's after the decimal point.

Answer choice A is the only logical value here.

Ans:  A

Bunuel · Answer

Similar question: https://gmatclub.com/forum/what-is-the- ... 23591.html

dave13 · Answer

how did you got 32 in numerator ?

pushpitkc · Answer

Hi  dave13

Formula:    (\frac{a}{b})^n = \frac{a^n}{b^n}

Here,  (\frac{2}{10})^5 = \frac{2^5}{10^5} = \frac{32}{100000} = 0.00032

Hope that helps you!

generis · Answer

dave13 - look at the numerator and the exponent. Does that help?

Abhishek009 · Answer

\frac{1}{5} = 0.2

No need to do decimal calculations,   2^5 = 32 , Answer will clearly be (A)

Andrewcoleman · Answer

such a great way to do this problem! light speed efficient!

ScottTargetTestPrep · Answer

(1/5)^5 = (0.2)^5 = 0.00032

Answer: A

VINO2493 · Answer

It can be written as :

(1/5)^5 = (2/10)^5 = 2^5/10^5 = 32/10^5

karnavora1 · Answer

\frac{1}{5}  when converted to a decimal becomes 0.2

2^5  is 32, you don't need to solve any further.

There is only 1 answer choice with 32 i.e. A

avigutman · Answer

In general, converting to a decimal is easiest when the denominator is some power of 10. In this case, unfortunately, the denominator only has five factors of 5. Let's expand the fraction by a matching number of 2s, so that the denominator will be a power of 10.
1/(5^5) = (2^5)/(10^5) = 0.00032 
Answer A.

ProKiller · Answer

Forget the calculation.

Just think about it for a minute... and build a thinking pattern from the easy calculations we know.

(1/5)^1 = 0.2 ... hmm. (1/5)^2 = (1/25) = 0.04 ... hmm... notice the pattern? .... (1/5)^n = (0.000... 2^n) .... At this stage, see the options. There is only one option which has (2^5) i.e. 32. Go ahead with option A... without worrying the number of zeroes after the decimal point. P.S: Had there been more than one option with 32, or option E saying "None of the above", we would worry about the number of zeroes.

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What is the decimal equivalent of (1/5)^2 ?

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What is the decimal equivalent of (1/5)^2 ?

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