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Digits problem

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Senior | Next Rank: 100 Posts
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by jfranco23 » Sat Mar 07, 2009 8:40 am
If d= 1/((2^3)x(5^7) is expressed as a terminating decimal, how many nonzero digits will d have?

A. One
B. Two
C. Three
D. Seven
E. Ten
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by loki.gmat » Sat Mar 07, 2009 10:34 am
i think it can have unlimited number of zeroes or may be i m missing something.


Thanks!
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by DanaJ » Sat Mar 07, 2009 10:54 am
First off, look at this: 2^3*5^3 = 10*3, thus making 1/(10^3) = 0.001.
Now, you're left with 5^4 = (5^2)^2 = 25^2 = 625. Then you should take the immediately greater power of 10 and divide it by 625:
1000/625 = 40/25 = 8/5 = 1.6.
This means that 1/625 will be a thousand times smaller than 1.6 or 0.0016.

Let's recap:
1/(2^3*5^3) = 0.001
1/(5^4) = 0.0016.
Multiply the two above to get that d = 0.0000016. As you can see, there are only two nonzero digits after the ".". This is why my answer will be B
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