Question

check each set that includes the number shown.
\\(\frac{5}{9}\\)
\\(\square\\) natural numbers
\\(\square\\) whole numbers
\\(\square\\) integers
\\(\square\\) rational numbers
\\(\square\\) irrational numbers
\\(\square\\) real numbers
done

Explanation:

Step1: Recall number set definitions

Natural numbers: Positive integers (1, 2, 3, ...). $\frac{5}{9}$ is not a natural number.
Whole numbers: Natural numbers + 0. $\frac{5}{9}$ is not a whole number.
Integers: Whole numbers + negative integers. $\frac{5}{9}$ is not an integer.
Rational numbers: Numbers expressible as $\frac{a}{b}$ (b≠0, integers a,b). $\frac{5}{9}$ fits, so it's rational.
Irrational numbers: Non - repeating, non - terminating decimals, not expressible as $\frac{a}{b}$. $\frac{5}{9}$ is not irrational.
Real numbers: Rational + irrational numbers. Since $\frac{5}{9}$ is rational, it's real.

Step2: Check each set

• Natural numbers: No.
• Whole numbers: No.
• Integers: No.
• Rational numbers: Yes (as $\frac{5}{9}=\frac{5}{9}$, a/b form).
• Irrational numbers: No.
• Real numbers: Yes (rational numbers are real).

Answer:

rational numbers, real numbers