Problem Solving

Rudy414 wrote:(10^8 - 10^2) / (10^7 - 10^3) is closest in value 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) [approximately]
= 10^1 = B

Cheers,
Brent