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2012 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

The number $0.2012$ is between

$\text{ (A) }\ 0 \text{ and } \frac{1}{10} \qquad\text{ (B) }\ \frac{1}{10} \text{ and } \frac{1}{5} \qquad\text{ (C) }\ \frac{1}{5} \text{ and } \frac{1}{4} \qquad\text{ (D) }\ \frac{1}{4} \text{ and } \frac{1}{3} \qquad\text{ (E) }\ \frac{1}{3} \text{ and } \frac{1}{2}$

Solution

Converting the fractions into decimals, we have:

$\frac{1}{10} = 0.1000$

$\frac{1}{5} = 0.2000$

$\frac{1}{4} = 0.2500$

$\frac{1}{3} = 0.\overline{3333}$

$\frac{1}{2} = 0.5000$

From these numbers, we can see that $0.2012$ is between $\boxed{\textbf{(C) } \frac{1}{5} \text{ and } \frac{1}{4}}$

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