Question

question 23

which of the following is an irrational number?

• pi (\pi)
• \frac{7}{8}
• 17
• 4.66666

Explanation:

Define rational and irrational numbers

Using the Rational Numbers and Number Classification knowledge points

• A rational number is any number that can be written as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b

eq 0\). In decimal form, rational numbers either terminate or repeat.

• An irrational number is a real number that cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating.

Analyze each option

Using the Rational Numbers and Number Classification knowledge points

• \(\text{Pi } (\pi)\): The mathematical constant \(\pi \approx 3.14159...\) has a non-terminating, non-repeating decimal expansion. It cannot be written as a fraction of two integers. Therefore, it is an irrational number.
• \(\frac{7}{8}\): This is explicitly written as a ratio of two integers, \(7\) and \(8\). Therefore, it is a rational number.
• \(17\): This integer can be written as \(\frac{17}{1}\). Therefore, it is a rational number.
• \(4.66666\): This is a terminating decimal (or a representation of a repeating decimal \(4.\bar{6} = \frac{14}{3}\)). In either case, it can be expressed as a fraction of two integers. Therefore, it is a rational number.

Answer:

• (A) Pi (\(\pi\)) (Correct answer)
• (B) \(\frac{7}{8}\)
• (C) 17
• (D) 4.66666