What characterizes an irrational number?

What characterizes an irrational number?

• A. It can be expressed as a fraction
• B. It is a repeating decimal
• C. It is non-terminating and non-repeating
• D. It is a terminating decimal

Answer: (C)

An irrational number is characterized by its nature of being non-terminating and non-repeating when expressed as a decimal. This means that the digits continue infinitely without settling into a repeating pattern. For example, the number pi (π) and the square root of 2 are both irrational numbers; their decimal expansions go on forever and do not exhibit any repeating sequences. In contrast, rational numbers can be expressed as fractions and can either be terminating or repeating decimals. Therefore, options that suggest an irrational number can be expressed as a fraction, or that it is a repeating or a terminating decimal, do not accurately describe the defining features of irrational numbers. Thus, the correct characterization hinges on the fact that irrational numbers are uniquely non-terminating and non-repeating in their decimal form.

An irrational number is characterized by its nature of being non-terminating and non-repeating when expressed as a decimal. This means that the digits continue infinitely without settling into a repeating pattern. For example, the number pi (π) and the square root of 2 are both irrational numbers; their decimal expansions go on forever and do not exhibit any repeating sequences.

In contrast, rational numbers can be expressed as fractions and can either be terminating or repeating decimals. Therefore, options that suggest an irrational number can be expressed as a fraction, or that it is a repeating or a terminating decimal, do not accurately describe the defining features of irrational numbers. Thus, the correct characterization hinges on the fact that irrational numbers are uniquely non-terminating and non-repeating in their decimal form.