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Not understanding the explanation for this

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by bmcewan » Sun Mar 16, 2014 3:53 pm
Can someone explain the answer? I don't quite understand the explanation in the book.

Question #111 in OG 13th edition - Problem solving.

If t=1/2^9 x 5^3 is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first nonzero digit to the right of the decimal point?

The answer is B.)Four
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by GMATGuruNY » Sun Mar 16, 2014 6:54 pm
If t= 1/(2^9 * 5^3) is expressed as a terminating decimal, how many zeros will t have between the decimal point and the first non zero digit to the right of the decimal point?

A - THREE

B - FOUR

C - FIVE

D - SIX

E - NINE

Determine how many powers of 10 are in the denominator.

1/(2�*5³) = 1 / (2�)(2³*5³) = 1/(64*10³) = 1/64,000.

Divide 64,000 into 1 and count the number of zeros:
Image
There are four 0's to the right of the decimal.

The correct answer is B.
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by Bill@VeritasPrep » Mon Mar 17, 2014 9:28 am
Alternatively, you could restate 1/(2^9 * 5^3) as 1/(10^3 * 2^6), or 1/1000 * 1/64. 1/64 will give you one zero on its own, and multiplying by 1/1000 will add three more.
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