Question

Which numbers are​ rational?
StartSet 0 comma eight sevenths comma StartFraction 13 Over 8 EndFraction comma negative 5 comma pi comma 6. 37 overbar comma 8 EndSet
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Part 1
Select all that apply.
A.6. 37 overbar
6. 37 overbar
B.
0
C.StartFraction 13 Over 8 EndFraction
StartFraction 13 Over 8 EndFraction
D.negative 5
negative 5
E.eight sevenths
eight sevenths
F.pi
pi
G.8
8
H.
There are no rational numbers.

Answer 1

Rational numbers are numbers that can be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \). Let's evaluate the numbers given:

- **0**: This can be expressed as \( \frac{0}{1} \), so it is rational.

- **eight sevenths**: This is \( \frac{8}{7} \), which is a fraction with integers, so it is rational.

- **StartFraction 13 Over 8 EndFraction**: This is \( \frac{13}{8} \), also a fraction with integers, so it is rational.

- **negative 5**: This can be expressed as \( \frac{-5}{1} \), so it is rational.

- **pi**: This is an irrational number and cannot be expressed as a fraction of integers, so it is not rational.

- **6.37 overbar**: The notation "overbar" typically indicates that the digits "37" repeat indefinitely (i.e., \( 6.373737...\)). This can be expressed as a fraction, so it is rational.

- **8**: This can be expressed as \( \frac{8}{1} \), so it is rational.

Based on this analysis, the rational numbers from the provided set are:

- **0**
- **eight sevenths**
- **StartFraction 13 Over 8 EndFraction**
- **negative 5**
- **6.37 overbar**
- **8**

So, the selections you should select are: **A, B, C, D, E, G**.