Problem Solving

The official question is:

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

Since the answer choices are so spread out, we can be quite aggressive with our estimation.

First, 10^8 - 10^2 can be rounded to 10^8
Is this reasonable? Well, 10^8 equals 100,000,000, so subtracting 10^2 (aka 100) from 100,000,000 still leaves us with about 100,000,000

Similarly, 10^7 - 10^3 can be rounded to 10^7 (10,000,000 - 1000 is pretty close to 10,000,000)

So, by estimating, we get:
(10^8 - 10^2)/(10^7 - 10^3) = (10^8)/(10^7)
= 10^1 = B

Cheers,
Brent