To determine the type of number that [tex]\(\frac{4}{9}\)[/tex] is, we can consider the definitions of the different types of numbers:
1. Whole Numbers: Whole numbers are non-negative integers including zero (0, 1, 2, 3, ...). A whole number must be an integer that is not negative.
2. Natural Numbers: Natural numbers are positive integers (1, 2, 3, ...). They are whole numbers that are positive and do not include zero.
3. Integers: Integers include all whole numbers and their negative counterparts (-3, -2, -1, 0, 1, 2, 3, ...).
4. Rational Numbers: Rational numbers are numbers that can be expressed as the quotient or fraction [tex]\(\frac{a}{b}\)[/tex] of two integers, with the denominator [tex]\(b\)[/tex] not equal to zero.
Let's check [tex]\(\frac{4}{9}\)[/tex] against these definitions:
1. Whole Number: [tex]\(\frac{4}{9}\)[/tex] is not a whole number because it is not a non-negative integer. It is a fraction and not an integer.
2. Natural Number: [tex]\(\frac{4}{9}\)[/tex] is not a natural number because it is not a positive integer. It cannot be counted as one of the natural numbers.
3. Integer: [tex]\(\frac{4}{9}\)[/tex] is not an integer because it is a fraction and does not represent a whole number.
4. Rational Number: [tex]\(\frac{4}{9}\)[/tex] can be expressed as the fraction [tex]\(\frac{4}{9}\)[/tex], where 4 and 9 are both integers, and the denominator is not zero. Hence, [tex]\(\frac{4}{9}\)[/tex] is a rational number.
Considering the results:
- Whole: No, because [tex]\(\frac{4}{9}\)[/tex] is not a non-negative integer.
- Natural: No, because [tex]\(\frac{4}{9}\)[/tex] is not a positive integer.
- Integer: No, because [tex]\(\frac{4}{9}\)[/tex] is not a whole number.
- Rational: Yes, because [tex]\(\frac{4}{9}\)[/tex] can be expressed as a fraction [tex]\(\frac{a}{b}\)[/tex], where a and b are integers, and b is not zero.
Therefore, [tex]\(\frac{4}{9}\)[/tex] is a rational number.
The types of numbers that [tex]\(\frac{4}{9}\)[/tex] falls into are:
[tex]\[ \text{rational} \][/tex]
The correct answer is:
[tex]\[ [5] \][/tex]
So, the only correct type that applies to [tex]\(\frac{4}{9}\)[/tex] is:
[tex]\[ \text{rational} \][/tex]
