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Example: What type of real numbers are these?

- Natural: positive whole numbers (e.g., 2, 34, 56)
- Whole: whole numbers without fractions, cannot be negative (e.g., 1, 98, 10)
- Integer: whole numbers that can be positive, negative, or zero (e.g., -5, -2, 45, 58)
- Rational: any whole number, fraction, or decimal that ends or repeats
- Irrational: any number that cannot be turned into a fraction

\begin{tabular}{c|c|c}
\hline
32 & 0 & -3 \\
\hline
[tex]$\frac{2}{3}$[/tex] & [tex]$\sqrt{100}$[/tex] & [tex]$\sqrt{17}$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To classify each of the given numbers according to their type, let's analyze them individually according to the definitions provided:

Step-by-step analysis of each number:

1. 32
- Natural: 32 is a positive whole number, so it fits this category.
- Whole: Every natural number is also a whole number.
- Integer: Since 32 is a whole number, it is also an integer.
- Rational: Any integer can be expressed as a fraction (32/1), making it a rational number.

2. 0
- Whole: 0 is considered a whole number.
- Integer: 0 is also classified as an integer.
- Rational: Since 0 can be expressed as a fraction (0/1), it is rational.

3. -3
- Integer: -3 is a whole number that can be positive or negative.
- Rational: -3 can be expressed as a fraction (-3/1), making it rational.

4. [tex]\( \frac{2}{3} \)[/tex]
- Rational: [tex]\(\frac{2}{3}\)[/tex] is a fraction, and all fractions are rational numbers.

5. [tex]\( \sqrt{100} = 10 \)[/tex]
- Natural: 10 is a positive whole number.
- Whole: 10 is a whole number.
- Integer: 10 is also an integer.
- Rational: Since 10 is an integer, it can be expressed as 10/1, making it rational.

6. [tex]\( \sqrt{17} \)[/tex]
- Irrational: The square root of 17 is not a perfect square, and its decimal form is non-repeating and non-terminating, so it is irrational.

Classifying the numbers:

```
+----+------------+-------+-------+-------------+------------+
| 32 | Natural | Whole | Integer | Rational | |
| 0 | | Whole | Integer | Rational | |
| -3 | | | Integer | Rational | |
| 2/3| | | | Rational | |
| 10 | Natural | Whole | Integer | Rational | |
| √17| | | | | Irrational |
+----+------------+-------+---------+-------------+------------+
```

The classification of the provided numbers are as follows:

- 32: Natural
- 0: Whole
- -3: Integer
- 2/3: Rational
- √100 (or 10): Whole
- √17: Irrational

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