What type of number cannot be expressed as a fraction?

What type of number cannot be expressed as a fraction?

• A. Rational number
• B. Whole number
• C. Irrational number
• D. Integer

Answer: (C)

The correct answer is that an irrational number cannot be expressed as a fraction. By definition, irrational numbers are real numbers that cannot be written as the ratio of two integers. This means they cannot be represented as a simple fraction (a/b, where a and b are integers and b is not zero). Common examples of irrational numbers include the square root of any non-perfect square (like √2 or √3) and the number π (pi). These numbers have non-repeating, non-terminating decimal expansions. For instance, π is approximately 3.14159..., and it goes on without repeating or terminating, illustrating its nature as an irrational number. In contrast, rational numbers, whole numbers, and integers can all be expressed as fractions. Rational numbers are defined as any number that can be represented in fraction form, including integers because any integer "n" can be expressed as n/1. Whole numbers are a subset of integers, including zero and positive integers, and they too can obviously be expressed in fraction form. Thus, the defining characteristic of irrational numbers sets them apart from these other categories.

The correct answer is that an irrational number cannot be expressed as a fraction. By definition, irrational numbers are real numbers that cannot be written as the ratio of two integers. This means they cannot be represented as a simple fraction (a/b, where a and b are integers and b is not zero).

Common examples of irrational numbers include the square root of any non-perfect square (like √2 or √3) and the number π (pi). These numbers have non-repeating, non-terminating decimal expansions. For instance, π is approximately 3.14159..., and it goes on without repeating or terminating, illustrating its nature as an irrational number.

In contrast, rational numbers, whole numbers, and integers can all be expressed as fractions. Rational numbers are defined as any number that can be represented in fraction form, including integers because any integer "n" can be expressed as n/1. Whole numbers are a subset of integers, including zero and positive integers, and they too can obviously be expressed in fraction form. Thus, the defining characteristic of irrational numbers sets them apart from these other categories.