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The value of (10^8-10^2)/(10^7-10^3) is closest to which of

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 25 Feb 2014, 20:53
10^8 is way too high from 10^2, similarly 10^7 is way too high from 10^3
No need to make any further simplification calculation, just calculate 10^8 / 10^7 = 10 = Answer = B
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 08 Mar 2014, 20:49
Option B.
Factor the numerator and denominator.
{[(10^4)-10] [10^4+10]}/10^3(10^4-1)
Taking 10 common from each term in numerator.
{10^2[(10^3-1)(10^3+1)]}/10^3[(10^2-1)(10^2+1)]

After further factorization and cancellation We're left with
(111*91)/10*101=9.99 or 10

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 09 Sep 2015, 10:27
I think the easiest way to solve this is to use the quotient rule. Since all bases are the same (10), split the problem into two fractions, use the quotient rule on each, then subtract.

(10^8-10^2)/(10^7-10^3) =

(10^8/10^7) - (10^2/10^3) =

10 - (10^-1) =

10 - (1/10) =

10 - 0.1 =

9.9 =

B.

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 11 Jan 2016, 15:18
Why we can't simply eliminate 10^8 with 10^7 and so on?

I did in this way and this is what I got:

1) 10^8 - 10^2 / 10^7 - 10^3;
2) I eliminate 10^8 with 10^7 and I got 10 on the up left side;
3) then I eliminate 10^2 with 10^3 and got zero on the up ritghtside and 10 on the down right side;
4) so, basically I left with 10 - 0 / - 10;
5) 10 / -10 = -1;
Because there isn't -1 on the answer choices I pick 1 that is the closest one.

What is wrong with my line of reasoning? I saw many times calculations involving exponents elimination if there is a division.

Thanks in advance for the explanation

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The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 07 Jan 2017, 22:45
As the question asks for approximation, let's tackle it in the same way :

Numerator : \(10^8-10^2\) : \(10^2\) is 0.00001% of \(10^8\) ,which is negligible when compared to \(10^8\)
denominator: \(10^7-10^3\) : \(10^3\) is 0.0001% of \(10^7\) ,which is negligible when compared to \(10^7\)

Hence ,(\(10^8\)) - (negligible) / (\(10^7\)) - (negligible)= \(10^8\)/\(10^7\) =10

Ans : B

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 09 Jan 2017, 15:29
\(\frac{10^{2}(10^{6} - {1})}{10^{3}(10^{4} - 1)}\)
\(\frac{10^{8}}{10^{7}}\)
10
B
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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 19 Jul 2017, 21:02
It is not

If you multiply the denominator by 10 you get very close to the numerator. No need to do exact calculatio

999999/99990

99990X10=999900 which is only 99 less than the numerator.

gmontalvo wrote:
I've run across several variants of the following question:
\(\frac{10^8 - 10^2}{10^7 - 10^3}\)

Here is the approach I want to take:
\(\frac{10^2(10^6 - 1)}{10^3(10^4 - 1)}\)

But when I cancel the numerator/demoninator what I am left with is kind of ugly.
\(\frac{999999}{99990}\)

Is there something I am missing? Is there a better way? Or should I just suck it up and do the division?

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 21 Jul 2017, 08:19
10^8-10^2 similar to 10^8
10^7-10^3 similar to 10^7
Now (10^8-10^2)/(10^7-10^3) will give us 10^8/10^7 i.e. 10.
Option B.

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of [#permalink]

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New post 08 Aug 2017, 22:07
jcbruin wrote:
The value of (10^8-10^2)/(10^7-10^3) is closest to which of the following?

A. 1
B. 10
C. 10^2
D. 10^3
E. 10^4

Any thoughts on the quickest way to solve? I factored out 10^2 in the numerator and 10^3 in the denominator.

Thanks!

\(\frac{(10^8-10^2)}{(10^7-10^3)}\)

\(\frac{10^2(10^6-1)}{10^3(10^4-1)}\)

'\(1\)' is very small value compared to \(10^6\) and \(10^4\), hence we can approximate value to \(10^6\) and \(10^4\). Therefore;

\(\frac{10^2*10^6}{10^3*10^4}\)

\(\frac{10^8}{10^7} = 10^{(8-7)} = 10^1 = 10\)

Answer (B)...

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Re: The value of (10^8-10^2)/(10^7-10^3) is closest to which of   [#permalink] 08 Aug 2017, 22:07

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