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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.

Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]

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04 Sep 2013, 06:33

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?

Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]

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05 Sep 2013, 22:57

1

This post received KUDOS

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.

Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]

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16 Nov 2013, 03:48

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.

Answer: A.

Hi Bunuel, Can you give another way to solve this? Sometimes your approach just doesn't jump to mind, and that's when I get stuck on questions such as this.... I wasn't able to see the approximation that you saw....

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

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06 Nov 2014, 15:20

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.

Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]

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14 Dec 2015, 07:12

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Re: In the decimal notation of number (2/23)^3. What is the thir [#permalink]

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03 Apr 2016, 04:52

sumande 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

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.

Bunel,

Even i have used this sort of method to calculate.

But is it reliable on all the cases?

Pls help

Thanks, A

gmatclubot

Re: In the decimal notation of number (2/23)^3. What is the thir
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03 Apr 2016, 04:52

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