Question

Name the rational numbers from the list below.
negative 9​, 0​, 38​, 6.32​, StartRoot 11 EndRoot​, StartRoot 25 EndRoot​, 4one ninth
​,minusStartFraction 10 Over 3 EndFraction
​, 1.4848848884...

Answer 1

To identify the rational numbers from the provided list, we need to recall that a rational number is any number that can be expressed as the quotient of two integers (i.e., a fraction) where the denominator is not zero.

Here are the numbers from your list examined for rationality:

1. **negative 9**: This is rational because it can be expressed as \(-\frac{9}{1}\).
2. **0**: This is rational because it can be expressed as \(\frac{0}{1}\).
3. **38**: This is rational as it can be expressed as \(\frac{38}{1}\).
4. **6.32**: This is rational because it can be rewritten as \(\frac{632}{100}\).
5. **StartRoot 11 EndRoot ( √11)**: This is not rational, as \( \sqrt{11} \) is an irrational number.
6. **StartRoot 25 EndRoot ( √25)**: This is rational because \(\sqrt{25} = 5\), which can be expressed as \(\frac{5}{1}\).
7. **4one ninth (4\frac{1}{9})**: This is rational. It can be expressed as \(\frac{37}{9}\).
8. **minusStartFraction 10 Over 3 EndFraction (−\frac{10}{3})**: This is rational.
9. **1.4848848884...**: This is an irrational number because it is a non-terminating, non-repeating decimal.

Thus, the rational numbers from the list are:
- negative 9
- 0
- 38
- 6.32
- √25 (which is 5)
- 4one ninth (4\frac{1}{9})
- minusStartFraction 10 Over 3 EndFraction (−\frac{10}{3})