Question

determine if the given number belongs to the set.
the number is \\(\frac{1}{9}\\). the sets are: natural (n) numbers, whole (w) numbers, integers (i), rational (q) numbers, irrational (s) numbers, real (r) numbers. there are checkboxes next to each set to determine membership for \\(\frac{1}{9}\\).

Explanation:

Step1: Analyze Natural Numbers (N)

Natural numbers are positive integers (1, 2, 3, ...). $\frac{1}{9}$ is a fraction, not a positive integer. So, $\frac{1}{9}
otin N$.

Step2: Analyze Whole Numbers (W)

Whole numbers include 0 and natural numbers. $\frac{1}{9}$ is not a whole number (0, 1, 2, ...). So, $\frac{1}{9}
otin W$.

Step3: Analyze Integers (I)

Integers are whole numbers and their negatives (... -2, -1, 0, 1, 2, ...). $\frac{1}{9}$ is not an integer. So, $\frac{1}{9}
otin I$.

Step4: Analyze Rational Numbers (Q)

Rational numbers are numbers that can be expressed as $\frac{a}{b}$ where $a, b \in \mathbb{Z}$ and $b
eq 0$. $\frac{1}{9}$ is in the form $\frac{a}{b}$ with $a = 1$, $b = 9$ (both integers, $b
eq 0$). So, $\frac{1}{9} \in Q$.

Step5: Analyze Irrational Numbers (S)

Irrational numbers cannot be expressed as a fraction of two integers. Since $\frac{1}{9}$ is a fraction of integers, it is not irrational. So, $\frac{1}{9}
otin S$.

Step6: Analyze Real Numbers (R)

Real numbers include all rational and irrational numbers. Since $\frac{1}{9}$ is rational, it is also real. So, $\frac{1}{9} \in R$.

Answer:

• Natural Numbers (N): No
• Whole Numbers (W): No
• Integers (I): No
• Rational Numbers (Q): Yes
• Irrational Numbers (S): No
• Real Numbers (R): Yes