Question

question 18

which of the following is an integer?

3.175
0
pi (\pi)
\frac{1}{4}

Explanation:

Define the set of integers

The set of integers, denoted by \(\mathbb{Z}\), consists of all whole numbers, their negative counterparts, and zero:

$$ \mathbb{Z} = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\} $$

Evaluate each given option

• \(3.175\): This is a terminating decimal, which is a rational number but not a whole number (not an integer).
• \(0\): Zero is a whole number and is explicitly included in the set of integers \(\mathbb{Z}\).
• \(\text{Pi } (\pi)\): This is an irrational number, approximately equal to \(3.14159\dots\), and is not an integer.
• \(\frac{1}{4}\): This is a non-integer fraction (rational number), equal to \(0.25\).

Identify the correct integer

Comparing the options to the definition of integers:

$$ 0 \in \mathbb{Z} $$

Answer:

• (A) 3.175
• (B) 0 (Correct answer)
• (C) Pi (\(\pi\))
• (D) \(\frac{1}{4}\)