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1 10 9 - 1 10 10 =

1 10 9 - 1 10 10 =


(A)

- 1 10


(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set O: Fractions & Decimals

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Posted: 08/03/2013 11:11
Can someone please explain the steps to this problem's solution?

First, I do not understand how 1/10^9 - 1/10^10 is equal to 1/10^9-1/10^9 * 1/10... There is a magnitude difference between these numbers that I thought would have to be multiplied out before subtracting these quantities, otherwise the remanded difference of 1/10 is not the same as 1/1000000000 minus 1/10000000000...?

Second, after someone explains why my logic above is insufficient for this equation, I am still unsure how 1/10^9 - 1/10^9 * 1/10 = 1/10^9(1-1/10)?

I appreciate the help!

Thank you.
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Posted: 08/04/2013 02:26
Hi Marshall,

In the given solution, we factored out the common fraction 1/10^9.

Let's also solve the problem by getting a common denominator. To that end, multiply top and bottom of the fraction 1/10^9 by 10. This yields

10/10^10

So, the original difference becomes

10/10^10 - 1/10^10

Since we now have the common denominator (bottom of the fraction) 10^10, we can write down that single denominator and subtract the numerators (top of the fraction):

(10 - 1)/10^10

Performing the subtraction yields

9/10^10

Hence, the answer is (D).

Since it's a little hard reading this explanation in text, we've also attached a graphic using standard mathematical notation.

Nova Press
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Posted: 09/02/2013 19:34
I understand how 10^9 is factored out but on the next step I don't see how we got the (1- 1/10). I looked at the other example and am still lost.
Arcadia
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Posted: 10/07/2013 17:54
Jennifer, try multiplying 1/10^9 back into (1 - 1/10), then you will understand.
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Posted: 12/09/2013 07:28
The answer choice is wrong. It should be -9/10^10 but you have -1/10^10.
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Posted: 12/09/2013 07:29
I mean 9/10^10
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Posted: 12/16/2013 16:57
Jigme, read the problem and solution again carefully.
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Posted: 01/31/2014 14:49
Jigme, you are right and we will correct it.
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Posted: 01/19/2014 16:53
As wet choice b and d are the same
Something is wrong with the answer
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Posted: 01/31/2014 14:47
Sorry, Asis, it will be corrected. The explanation is correct though.
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1 10 9 - 1 10 10 = 
Posted: 07/09/2014 17:40
I'm not understanding how 10^10 with a line underneath it, constitutes the answer: 9/10^10...

Maybe it's just my iPad that could be showing the options incorrectly, due to compatibility issues, but then that would be the first time because this app has been working great so far.
Contributor
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Posted: 07/09/2014 18:13
Reply: Melissa, it's a formatting issue on our end. We switched to MathML and it's been causing issues. We will fix it but yeah the display is in error for answer D
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1 10 9 - 1 10 10 = 
Posted: 09/23/2014 12:43
Yeah this is still an issue 3 month later here in September. Can we get on these fixes?
Arcadia
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Posted: 09/23/2014 14:10
Thks Darren. It renders correctly on the website: http://www.arcadiaprep.com/discussion/messages/889

We are pushing the bug fix to the apps right now. Thanks for using the app, and sorry for the inconvenience.
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