Question

Determine whether each statement below is true or false.(5 points)
True False
-9 is a whole number.


2/3
is a rational number.


64−−√
is a rational number.


0 is a natural number.


π
is an irrational number.

Answer 1

Let's evaluate each statement:

1. **-9 is a whole number.**
**False.** Whole numbers are non-negative integers: 0, 1, 2, 3, ... -9 is negative.

2. **2/3 is a rational number.**
**True.** Rational numbers can be expressed as the quotient of two integers, where the denominator is not zero. 2/3 fits this definition.

3. **64−−√ is a rational number.**
**True.** The square root of 64 is 8, which is a whole number and therefore rational.

4. **0 is a natural number.**
**False.** By common convention, natural numbers are the positive integers: 1, 2, 3, ... Some definitions include 0, but the most prevalent definition does not.

5. **π is an irrational number.**
**True.** π (pi) cannot be expressed as a fraction of two integers, making it an irrational number.

So the evaluations are:

- -9 is a whole number: **False**
- 2/3 is a rational number: **True**
- 64−−√ is a rational number: **True**
- 0 is a natural number: **False**
- π is an irrational number: **True**