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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]

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New post Updated on: 31 Dec 2012, 04:31
2
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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

Originally posted by vshaunak@gmail.com on 30 Jun 2007, 08:49.
Last edited by Bunuel on 31 Dec 2012, 04:31, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In the decimal notation of number (2/23)^3. What is the thir  [#permalink]

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New post 31 Dec 2012, 04:35
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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.

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

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

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New post 05 Sep 2013, 22:57
2
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]

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New post 16 Nov 2013, 03:48
1
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....
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Re: In the decimal notation of number (2/23)^3. What is the thir  [#permalink]

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New post 22 Nov 2013, 05:22
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]

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

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

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New post 18 Feb 2018, 12:19
3
1
Simple and quickest approach:

(2/23) - > (0.0x..) no need to calculate after x

(0.0x..)^3 -> (0.000z....) (one 0 will multiply 3 times when cubed)

Therefore the third digit after the decimal point is 0.
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Re: In the decimal notation of number (2/23)^3. What is the thir  [#permalink]

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New post 14 Mar 2019, 08:19
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.



Didn't get this at all:
"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.
"

How can you say that just because it is 1 in another case, it will be 0 in another number which is shorter? I am missing something.
Can you please explain in detail? Thanks.
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Re: In the decimal notation of number (2/23)^3. What is the thir  [#permalink]

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New post 14 Mar 2019, 08:29
1
Akshit03 wrote:
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.



Didn't get this at all:
"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.
"

How can you say that just because it is 1 in another case, it will be 0 in another number which is shorter? I am missing something.
Can you please explain in detail? Thanks.


Check any positive number less than 0.001. You'll see that the third digit to the right of the decimal point will be 0.
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Re: In the decimal notation of number (2/23)^3. What is the thir  [#permalink]

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New post 13 Jun 2019, 11:25
1
Hi,

Is there any other way to solve this question?
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Re: In the decimal notation of number (2/23)^3. What is the thir   [#permalink] 13 Jun 2019, 11:25
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