Use the theorem below to answer the question that follows.

If the sum of a number's digits is divisible by three, the number is divisible by three.

Which of the following ways of expressing a three digit number,n,best demonstrates why this theorem is true?

A. $\displaystyle n = a(10^2) + b(10) + c$

B. $\displaystyle n = a(100) + b(10) + c$

C. $\displaystyle n = a(99 + 1) + b(9 + 1) + c$

D. $\displaystyle n = a(300-200) + b(30-20) + c(9-8)$