Question

Determine whether each statement below is true or false.(5 points)True False23is a rational number.-9 is a whole number.64−−√is a rational number.πis an irrational number.0 is a natural number.

Answer 1

Let's evaluate each statement one by one:

1. **23 is a rational number.**
**True** - A rational number is defined as any number that can be expressed as a fraction of two integers, where the denominator is not zero. Since 23 can be expressed as \( \frac{23}{1} \), it is a rational number.

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

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

4. **π is an irrational number.**
**True** - The number π (pi) is a well-known irrational number, meaning it cannot be expressed as a fraction of two integers, and its decimal representation is non-terminating and non-repeating.

5. **0 is a natural number.**
**False** - The definition of natural numbers varies, but traditionally, natural numbers are the set of positive integers (1, 2, 3, ...). Some definitions include 0, but in most standard contexts, 0 is not considered a natural number.

Summary of answers:
1. True
2. False
3. True
4. True
5. False