User:Anabel.disher/Sandbox/Prob 8

2012 CEMC Gauss (Grade 8) Problems/Problem 8‎

Problem

The number $0.2012$ is between

$\text{ (A) }\ 0 \text{ and } \frac{1}{10} \qquad\text{ (B) }\ 120^{\circ} \qquad\text{ (C) }\ 30^{\circ} \qquad\text{ (D) }\ 300^{\circ} \qquad\text{ (E) }\ 180^{\circ}$

Solution

Converting the fractions into decimals, we have:

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

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

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

$\frac{1}{3} = \overline{0.3333}$

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

From these numbers, we can see that $0.2012$ is between $\boxed{\textbf{(C) }30^{\circ}}$

This problem is kind of unclear because $0.2012$ is just a decimal number, but most of the answer choices are angles in degrees. The only option that’s a plain number interval is between $0$ and $\frac{1}{10}$ , but since $0.2012$ is bigger than $0.1$ , it doesn’t fit there.

The other choices are angles, so maybe the problem expects us to compare the decimal to the angle’s value in radians, but it doesn’t say that anywhere. Without explaining that, it’s confusing to know what the problem really wants.

So yeah, it feels like something is missing or left out.

--Aoum (talk) 19:37, 17 June 2025 (EDT)

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User:Anabel.disher/Sandbox/Prob 8

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