Question

Determine whether each statement below is true or false.(5 points)
True False
23 is a rational number.


-9 is a whole number.


0 is a natural number.


64−−√ is a rational number.


π is an irrational number.

Answer 1

Let's evaluate each statement:

1. **23 is a rational number.**
**True** - A rational number is any number that can be expressed as a fraction of two integers. Since 23 can be expressed as \( \frac{23}{1} \), it is a rational number.

2. **-9 is a whole number.**
**False** - Whole numbers are the set of non-negative integers (0, 1, 2, 3, ...). Since -9 is negative, it is not a whole number.

3. **0 is a natural number.**
**False** - Natural numbers are typically defined as the set of positive integers starting from 1 (1, 2, 3, ...). However, some definitions include 0 in the set of natural numbers. In standard definitions, 0 is not considered a natural number.

4. **\(\sqrt{64}\) is a rational number.**
**True** - \(\sqrt{64} = 8\), which is a whole number and hence also a rational number.

5. **π is an irrational number.**
**True** - π (pi) is known to be an irrational number because it cannot be expressed as a fraction of two integers.

To summarize:
1. True
2. False
3. False
4. True
5. True