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# In the decimal notation of number (2/23)^3. What is the thir

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In the decimal notation of number (2/23)^3. What is the thir [#permalink]  30 Jun 2007, 07:49
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Question Stats:

66% (02:05) correct 34% (01:32) wrong based on 250 sessions
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Dec 2012, 03:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: PS Decimal digits [#permalink]  30 Jun 2007, 07:56
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vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?

The first digit after the decimal point in (2/23) is 0. That is something like 0.0x, which is equal to 0.x * (10^-1). Therefore, the third power will be (0.x)^3 * (10^-3). And, hence, the third digit to the right of the decimal point is 0. Choice A.
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Re: PS Decimal digits [#permalink]  30 Jun 2007, 11:17
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?

i believe in such cases, we need to identify the answer quickly because such questions have obvious answer.

for ex: if it is 5:20 now, what was the time 367,210 minuets earlier?

in this case, if the answers are: 2:05, 2:10, 2:26, 2:31 and 2:45.

2:10 is obvious answer because we need to deduct 10 minuets from 20 minuets.

even if the answers are: 2:00, 2:10, 2:20, 2:30 and 2:40, the correct one is 2:10 because deducting 10 from 20 can never be other than 10.

therefore, i think we need find whether the question asks calculation or some quick tricks.
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Re: PS Decimal digits [#permalink]  30 Dec 2012, 20:54
Himalayan wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?

i believe in such cases, we need to identify the answer quickly because such questions have obvious answer.

for ex: if it is 5:20 now, what was the time 367,210 minuets earlier?

in this case, if the answers are: 2:05, 2:10, 2:26, 2:31 and 2:45.

2:10 is obvious answer because we need to deduct 10 minuets from 20 minuets.

even if the answers are: 2:00, 2:10, 2:20, 2:30 and 2:40, the correct one is 2:10 because deducting 10 from 20 can never be other than 10.

therefore, i think we need find whether the question asks calculation or some quick tricks.[/quote]

Dear Club members

I didn't understand why we deducted 10 minutes from 20. Can someone please elaborate.

Thank you
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Piyush Jain

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Re: In the decimal notation of number (2/23)^3. What is the [#permalink]  30 Dec 2012, 22:04
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

a. 0
b. 1
c. 2
d. 4
e. 8

Is there any quick approach without solving it completely?

quicker way:

(2/23)^3 can be written as (25-23/23)^3 and hence (25/23-1)^3>>(1.08XYZ-1)^3>>>0 should be third digit
Math Expert
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  31 Dec 2012, 03:35
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Expert's post
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vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8

Notice that $$(\frac{2}{23})^3<(\frac{2}{20})^3$$.

Now, $$(\frac{2}{20})^3=(\frac{1}{10})^3=0.001$$.

Finally, since $$(\frac{2}{23})^3<0.001$$, then the third digit to the right of the decimal point of $$(\frac{2}{23})^3$$ is 0.

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Math Expert
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Kudos [?]: 41139 [0], given: 5672

Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  04 Sep 2013, 02:47
Expert's post
Bumping for review and further discussion.
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  04 Sep 2013, 05:33
Is there a recommended spot to conceptually study how to approach problems like this?

How to notice these situations and to approximate as Bunuel did, ya know? Is Bunuel's approach the preferred method or is there a "book" approach to these styles of questions?
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  05 Sep 2013, 21:57
1
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IvanW wrote:
Is there a recommended spot to conceptually study how to approach problems like this?

How to notice these situations and to approximate as Bunuel did, ya know? Is Bunuel's approach the preferred method or is there a "book" approach to these styles of questions?

There can be numerous ways to solve such questions. IMO, Bunuel approach is the best and you should follow that. But, end of the day what strikes you under timed conditions is the what matters. I suggest, to develop acumen for such questions, follow Bunuel and understand his approach for every question he responds to. 90% of times you will find that he has solved the questions in a much easier way. Initially, you will find his approach too hard to digest, but when you keep on seeing his methods, you will probably start thinking on the same lines.

Hope it helps!
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  16 Nov 2013, 02:48
Bunuel wrote:
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8

Notice that $$(\frac{2}{23})^3<(\frac{2}{20})^3$$.

Now, $$(\frac{2}{20})^3=(\frac{1}{10})^3=0.001$$.

Finally, since $$(\frac{2}{23})^3<0.001$$, then the third digit to the right of the decimal point of $$(\frac{2}{23})^3$$ is 0.

Hi Bunuel,
Can you give another way to solve this?
I get stuck on questions such as this....
I wasn't able to see the approximation that you saw....
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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]  22 Nov 2013, 04:22
vshaunak@gmail.com wrote:
In the decimal notation of number (2/23)^3. What is the third digit to the right of the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8

(2/23)^3 = (2^3)* (1/23)^3 = 8 * (0.05^3). Third digit will be 0.
Cheers!
J
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In the decimal notation of number (2/23)^3. What is the thir [#permalink]  06 Nov 2014, 14:20
I got stuck and just couldn't find the shortcut to this question so I just tried the dumb method of doing long division. 23^3 took me 10 seconds, 2^3 was memorized. As soon as I tried long division of 8/12167, I figured out the trick. There were a lot of zeros before I could reach a number large enough to be divided by 12167 even once.

For anyone who still don't get it, just try solving the problem the dumb way by finding the numerator, denominator, and then doing long division. This question is one of those questions that you just have to start doing to understand what the "trick" is.
In the decimal notation of number (2/23)^3. What is the thir   [#permalink] 06 Nov 2014, 14:20
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