List the elements of the given set that are rational numbers. $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$
A) $0 , - 8,100,22 / 7,1 . \overline { 23 } , - \frac { 1 } { 9 }$
B) $0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$
C) $0 , - 8,100,22 / 7,1 . \overline { 23 } , \sqrt [ 3 ] { 4 }$
D) $0 , - 8,100$
E) $22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 }$

Question

Quizplus · Accepted Answer

A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. Using this definition, we can identify that the following elements of the set are rational numbers:
- $0$ (can be expressed as $0/1$)
- $-8$ (can be expressed as $-8/1$)
- $100$ (can be expressed as $100/1$)
- $22/7$ (fraction form that can be simplified as $3\frac{1}{7}$)
- $1.\overline{23}$ (a repeating decimal that can be expressed as $1\frac{23}{99}$)
- $-\frac{1}{9}$ (can be expressed as $-1/9$)

Therefore, the best choice is A as it only includes the rational numbers from the given set.

List the Elements of the Given Set That Are Rational {0,−8,100,22/7,5,1.23‾,−19,43}\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}{0,−8,100,22/7,5​,1.23,−91​,34​}

List the Elements of the Given Set That Are Rational $\left\{ 0 , - 8,100,22 / 7 , \sqrt { 5 } , 1 . \overline { 23 } , - \frac { 1 } { 9 } , \sqrt [ 3 ] { 4 } \right\}$