Question

Which of the following is true about the number $0.66\overline{66}$?

• A. It is a rational number
• B. It is an irrational number
• C. It is correctly gridded as $".66"$
• D. It is equivalent to $\frac{67}{100}$
• E. None of the above.

Answer 1

The correct option is A It is a rational number

Since $0.66\overline{66}=\frac{2}{3}$, and any fraction with integers on the top and bottom is a rational number, answer A is correct. Why are the other answers incorrect? The number $\frac{2}{3}$ can be correctly gridded as $.666$ or $.667$ or $\frac{2}{3}$ but not as $0.66$. Also, $\frac{67}{100}=0.67$ is not the same as $0.66\overline{66}$.