Estimating maths problems exponents and fractions?

Question

I have a little query, for my upcoming exam I am expected to be able to give approximate answers to equations like this...
1/(2.03)^4

The explanation given is:

1/(2.03)^4 ~ 1/16+(0.03 x -1/8) = 47/800

The second example is

1/(2.97)^3 ~ 1/27+(0,03 x -1/27) = 103/2700

I understand all except the part in the second brackets and how the numbers are found. Im studying this course in French and this is not my first language, i was wondering if somebody could explain it in English please?

Answer 1

The .03 is of course the amount by which the estimate was in error. Where the 1/8 and 1/27 come from, I don't know. But I do know the second example should be (.03 +1/27) and not (.03-1/27).

In the 1st example we selected 2 as our 1st guess which would make our answer too big so we had to adjust it by lowering it by -3/800.

In the 2nd example, our estimate of 3 made the answer too small so we had to RAISE it by an amount 3/2700. This is why the minus sign is wrong in your example.

Sorry I can't figure out where the numbers 1/8 and 1/27 come from. The only thing I notice is that in example the 1/8 is twice the original estimate of 1/16, while in the second example, the 1/27 is equal to the initial estimat of 1/27.

Answer 2

Can u plz post this question on http://www.tutorbuddy.org I will answer when you post