Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #16

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# If is expressed as a terminating decimal

If is expressed as a terminating decimal, how many nonzero digits will the decimal have? One, Two, Four, Six, Eleven

### 4 Explanations

2

Aug 5, 2018 • Comment

Sam Kinsman

Hi Nipun,

Keep in mind if we have two different numbers that are raised to the same power, such as a^x * b^x, we can group the base numbers together. So:

a^x * b^x = (a * b)^x = ab^x

2^(11) * 5^(11) = (2 ^ 5)^11 = 10^(11)

I hope this helps!

yaser reda

There is an easier shortcut: we could multiply the numerator and the denominator by 2 to power 6. Then, the numerator will be 64 while the denominator will be 10 to power 17.

That works too! Good solution :)

1

Robert Clemons

Can you assume that because 1 / 5^6 has two repeating decimals that if you multiplied this by 1 / 10^11 it would have the same number?

Feb 17, 2018 • Comment

David Recine

Yes, there'd be the same number of nonzero digits and the nonzero digits would still be 6 and 4. Effectively, you'd be dividing the original decimal value of 1/(5^2) by 10^11, which would mean 11 additional zeroes would be added between the decimal point and 64.

1

Arturo Garcia

Can you please elaborate on how you made the 5 a 1/5 fraction

Mar 21, 2017 • Comment

Hi Arturo! First, note that the 5 is already in the denominator of the fraction, so we're not changing 5 to 1/5. We have 1 / (5^6), and we can change that to (1/5)^6 = 0.2^6. Note that we can only change 1 / (5^6) to (1/5)^6 because we have a 1 in the numerator.

12

Chris Lele

Oct 11, 2012 • Comment

sarah herschede

Why are you allowed to raise (1/5) to the 6th power? Is this allowed for any number in the numerator or only 1? Thanks

how many nonzero digit does a number like 0.0010100 have?

Hi Sarah! Good question. This is allowed only because we have a 1 in the numerator, which is always going to be 1.