Bunuel wrote:
fireinbelly wrote:
Which of the following is closest to \(\frac{4}{2.001}\)?
A. 1.997
B. 1.998
C. 1.999
D. 2.000
E. 2.001
I have seen some questions where if the value is .001 or very small value then we usually ignore that value...however the answer seems to be C? why cant we say that 4/2.001 is very close to 4/2 as .001 is negligible here hence the answer would be D in that case. Can someone please help me understanding this concept? Thanks.
M24-07
\(\frac{4}{2.001}=\frac{4}{2+0.001}=\frac{4(2-0.001)}{(2+0.001)(2-0.001)}=\frac{4(2-0.001)}{4-0.001^2}\).
Now, since \(0.001^2\) is very small number then \(4-0.001^2\) is very close to 4 itself, so \(0.001^2\) is basically negligible in this case and we can write: \(\frac{4(2-0.001)}{4-0.001^2} \approx \frac{4(2-0.001)}{4}=2-0.001=1.999\).
Answer: C.
Hi Bunuel,
Thanks for the solution. I understood the way to approach it and why the answer is C.
I have a small query - while solving as you mentioned that 4 - 0.002^2 is equal to 4 only because 0.002^2 is negligible here....However in the main question where 2 - 0.002 is written 0.002 is not negligible.
Is it not negligible only because it is not sufficiently smaller no.? If it were 0.002^2 in the main question instead of 0.002 then could that have been negligible?
Please share your valuable inputs.