0.99999999/1.0001 - 0.99999991/1.0003 =

\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)


(A) \(10^{(-8)}\)

(B) \(3*10^{(-8)}\)

(C) \(3*10^{(-4)}\)

(D) \(2*10^{(-4)}\)

(E) \(10^{(-4)}\)


OG 2019 #215 PS00574

\(\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=\)


(A) \(10^{(-8)}\)

(B) \(3*10^{(-8)}\)

(C) \(3*10^{(-4)}\)

(D) \(2*10^{(-4)}\)

(E) \(10^{(-4)}\)



OG 2019 #215 PS00574

chetan2u VeritasKarishma Gladiator59 Bunuel generis

Hi Experts -- i see the answer is D in this question but i do have a question regarding "Estimating" this

Give estimation is a strategy for the GMAT -- i estimated :

1.0001 == estimated down to 1.0000
1.0003 == estimated down to 1.0000

Hence i was left with

\(\frac{0.99999999}{1}\) - \(\frac{0.99999991}{1}\) =

0.99999999 −0.99999991 =0.00000008 or 8 * \(10^{-8}\)

Question : why isn't the estimation method getting me close /somewhat close to option D ...option D seems 1000 times larger than my estimation (option B and option C sees closer)

Any idea where the logic is wrong in this case for such a HUGE difference ?

Note that all the numbers are very close to 1. So you cannot estimate some of them to 1 and not others. All options are very very close to each other too. So you cannot estimate here.

Hi karishma

Thank you so much for replying

Understand every answer is close to 1

But you would agree though the estimation method is OFF by times 1000 compared to option D

Any idea why the estimation is so off by any chance

I think every one would make the estimation that 1.0001 can be written up as 1.0000 and the same with 1.0003 as 1.0000

Posted from my mobile device

Responding to a pm:
To be honest, I can't think of an alternative method. The fractions are really complicated and need to be simplified before proceeding. For simplification, I think you will need to use a^2 - b^2 = (a - b)(a + b)

All I can suggest is that you can try to solve it without the exponents if that seems easier e.g.

\(\frac{0.99999999}{1.0001}-\frac{.99999991}{1.0003}\)

\(\frac{{1 - .00000001}}{{1 + .0001}}-\frac{{1 - .00000009}}{{1 + .0003}}\)

\(\frac{{1^2 - .0001^2}}{{1 + .0001}}-\frac{{1^2 - 0.0003^2}}{{1 + .0003}}\)

\(\frac{{(1 - .0001)(1 + .0001)}}{{(1 + .0001)}}-\frac{{(1 - .0003)(1 + .0003)}}{{(1 + .0003)}}\)

\((1 - .0001) - (1 - .0003)\)

\(.0002 = 2*10^{-4}\)

KarishmaB
This is very helpful, thank you! To clarify my understanding of scientific notation...why is it that we do not count the zero when moving the decimal place right and left for expanding scientific notation? Is my understanding correct that you always start at the first non-zero number?

For example, I know that:
10^-4=0.0001 (but I get stuck because I would think you start at the zero in moving over the decimal e.g., to get .001)
and
10^4=10,000 (but I get stuck because I would think you start at the zero again to get 100,000)

Thank you again