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Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
20 Dec 2012, 05:12

14

This post received KUDOS

Expert's post

9

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Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
17 Aug 2013, 18:02

Bunuel wrote:

Bumping for review and further discussion.

Bunuel I actually, do have question.

The expression is equal to 1/(2*5)^3(5^4)=1/625,000. Knowing this expression alone. Is there a way to figure out the answer? Just didn't occur to me to multiply by 2^4

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
21 Oct 2013, 00:59

Bunuel wrote:

Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.

Is there any other method to do it . I mean it is difficult to think of 2^4 there and then .

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
29 Dec 2013, 11:57

Bunuel wrote:

Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
29 Dec 2013, 12:00

1

This post received KUDOS

Expert's post

theGame001 wrote:

Bunuel wrote:

Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.

I have seen couple of more problem like this. One thing is still not clear to me. When you multiply whole denominator by 2^4 why is 5^7 getting ignored? Shouldn't 2^4 multiply both 2^3 as well as 5^7?

Thanks

Frankly, the red part does not make any sense...

The denominator is \(2^7*5^7\). Multiply it by \(2^4\). What do you get? _________________

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
11 Mar 2014, 15:54

Bunuel wrote:

Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.

Re: If d=1/(2^3*5^7) is expressed as a terminating decimal, how [#permalink]
11 Mar 2014, 22:36

1

This post received KUDOS

Expert's post

WinterIsComing wrote:

Bunuel wrote:

Walkabout wrote:

If d=1/(2^3*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

Given: \(d=\frac{1}{2^3*5^7}\).

Multiply by \(\frac{2^4}{2^4}\) --> \(d=\frac{2^4}{(2^3*5^7)*2^4}=\frac{2^4}{2^7*5^7}=\frac{2^4}{10^7}=\frac{16}{10^7}=0.0000016\). Hence \(d\) will have two non-zero digits, 16, when expressed as a decimal.

Answer: B.

What is it that you saw that indicated you should multiply by 2^4. Just looking at the problem that never occurred to me and I'd like to understand why it did to you.

We need to multiply by 2^6/2^6 in order to convert the denominator to the base of 10 and then to convert the fraction into the decimal form: 0.xxxx.

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