2002 AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

The ratio

\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}

is closest to which of the following numbers?

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Solution

Factoring gives

\dfrac{10^{2000}(1+100)}{2\cdot 10^{2001}}=\dfrac{101}{20}=5.05,

which is closest to

5.

Thus, the correct answer is D.

Concepts: exponent · estimation

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