Reducing Powers

lukeposada wrote:Need some help understanding this one:

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
the answer is b

It's important to note that the question asks us to to find the closest value here.

The fast approach is to recognize that 10^8 (100 billion) is wayyyyyyyyyyy larger than 10^2 (100). In fact 10^2 is quite insignificant compared to 10^8

So, 10^8 - 10^2 is pretty close in value to 10^8 (Aside: If you had $100 billion dollars and you lost $100 dollars, you still pretty much have $100 billion dollars)

The same applies to 10^7 - 10^3 (10^7=10 billion, and 10^3=1000). So, 10^7 - 10^3 is pretty close to 10^7

So, (10^8 - 10^2)/(10^7 - 10^3) is very close to (10^8)/(10^7) and (10^8)/(10^7) = 10^1 = 10

Choose B.