List the elements of $\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 } \right\}$ that belong to the set of rational numbers.
A) $- 3,0,1,2,9$
B) $\sqrt { 5 } , \pi$
C) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1,2,4.45,9,16 . \overline { 6 }$
D) $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 }$
E) $0,1,2,9$

Question

Quizplus · Accepted Answer

A number is rational if and only if it can be expressed as a ratio of two integers. Therefore, the only numbers in the set that are rational are those whose decimal representation is either a terminating decimal or a repeating decimal. We can see that the only numbers in the set that fit this description are: $- 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1,2,4.45,9,16 . \overline { 6 }$. Thus, the answer is $\boxed{	extbf{(C)}}$.

List the Elements Of {−3,−83,0,23,1,5,2,π,4.45,9,16.6‾}\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 } \right\}{−3,−38​,0,32​,1,5​,2,π,4.45,9,16.6}

List the Elements Of $\left\{ - 3 , - \frac { 8 } { 3 } , 0 , \frac { 2 } { 3 } , 1 , \sqrt { 5 } , 2 , \pi , 4.45,9,16 . \overline { 6 } \right\}$