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The decimal .1 is how many times greater

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The decimal .1 is how many times greater  [#permalink]

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New post 28 Mar 2015, 09:14
3
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A
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D
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Question Stats:

70% (00:58) correct 30% (00:57) wrong based on 139 sessions

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The decimal .1 is how many times greater than the decimal (.001)^3?
A) 10
B) 10^2
C) 10^5
D) 10^8
E) 10^10

Source: GMAT Nova

I tried it as follows -
suppose .1 is x times greater than the decimal (.001)^3
then we can write -
.1 * x = (.001)^3
now when I solved for x I got 1/10^8 as answer which is incorrect. Can someone help me understand what did I do wrong?
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Re: The decimal .1 is how many times greater  [#permalink]

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New post 28 Mar 2015, 11:45
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Hi fireinbelly,

This type of question is sometimes called a "decimal shift" question, since the individual digits in the two values are the same, but the position of the decimal has been shifted.

Here, we're asked to compare 0.1 to (.001)^3

The first step is to figure out what (.001)^3 is....

(.001)(.001)(.001) has 9 decimal points and (1)(1)(1) = 1, so we're dealing with a 9-digit decimal with a "1" at the end:

I've added the two spaces to make it easier to read.
.000 000 001

Every time we multiply by 10, we 'shift' the decimal one spot to the 'left'.

To get from this value (with its 9 decimal points) up to .1 (with its 1 decimal point), we have 'shift left' 8 times. In other words, we have to multiple by 10^8.

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Re: The decimal .1 is how many times greater  [#permalink]

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New post 29 Mar 2015, 07:19
1
fireinbelly wrote:
The decimal .1 is how many times greater than the decimal (.001)^3?
A) 10
B) 10^2
C) 10^5
D) 10^8
E) 10^10

Source: GMAT Nova

I tried it as follows -
suppose .1 is x times greater than the decimal (.001)^3
then we can write -
.1 * x = (.001)^3
now when I solved for x I got 1/10^8 as answer which is incorrect. Can someone help me understand what did I do wrong?



0.001 contains 3 digits after decimal.
Hence (0.001)^3 contains 3*3 = 9 digits after decimal i.e. 0.000000001.

We need to know how many times is 0.1 greater than 0.000000001.
So we need ratio of 0.1/0.000000001
= 10^(-1)/10^(-9)
= 10^9/10^1
= 10^8

Hence option (D).

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Re: The decimal .1 is how many times greater  [#permalink]

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New post 17 Oct 2017, 09:20
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The decimal .1 is how many times greater &nbs [#permalink] 17 Oct 2017, 09:20
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