Question

Which numbers are​ rational?
StartSet 5. 35 overbar comma pi comma 9 comma eight sevenths comma 0 comma StartFraction 12 Over 7 EndFraction comma negative 9 EndSet
Question content area bottom
Part 1
Select all that apply.
A.eight sevenths
eight sevenths
B.StartFraction 12 Over 7 EndFraction
StartFraction 12 Over 7 EndFraction
C.negative 9
negative 9
D.pi
pi
E.
0
F.5. 35 overbar
5. 35 overbar
G.9
9
H.
There are no rational numbers.

Answer 1

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Let’s evaluate each of the numbers given:

A. **eight sevenths** - \( \frac{8}{7} \) is rational.
B. **StartFraction 12 Over 7 EndFraction** - \( \frac{12}{7} \) is rational.
C. **negative 9** - \(-9\) can be expressed as \( \frac{-9}{1} \), so it is rational.
D. **pi** - \(\pi\) is an irrational number and cannot be expressed as a fraction of two integers, so it is not rational.
E. **0** - \(0\) can be expressed as \( \frac{0}{1} \), so it is rational.
F. **5. 35 overbar** - This indicates a repeating decimal \( 5.353535...\), which can be expressed as a fraction, so it is rational.
G. **9** - \(9\) can be expressed as \( \frac{9}{1} \), so it is rational.
H. **There are no rational numbers** - This statement is incorrect.

### Conclusion
The rational numbers from the list are:
- A. eight sevenths
- B. StartFraction 12 Over 7 EndFraction
- C. negative 9
- E. 0
- F. 5. 35 overbar
- G. 9