Irrational Numbers are decimals that do not terminate or repeat. Which option best reflects this?

Irrational Numbers are decimals that do not terminate or repeat. Which option best reflects this?

• A. Decimals that do not terminate or repeat.
• B. They terminate but don't repeat
• C. They can be expressed as fractions
• D. They are decimals that terminate

Answer: (A)

Irrational numbers have decimal expansions that never end and never settle into a repeating pattern. That continuous, nonrepeating trail of digits is exactly what the option describes: decimals that do not terminate or repeat. For example, sqrt(2) is about 1.41421356... and goes on without repeating, and pi likewise goes on without a repeating block. In contrast, terminating decimals end after a finite number of digits, and repeating decimals settle into a repeating block; both of these are rational. So the statement that best reflects irrational numbers is the one describing decimals that do not terminate or repeat.

Irrational numbers have decimal expansions that never end and never settle into a repeating pattern. That continuous, nonrepeating trail of digits is exactly what the option describes: decimals that do not terminate or repeat. For example, sqrt(2) is about 1.41421356... and goes on without repeating, and pi likewise goes on without a repeating block. In contrast, terminating decimals end after a finite number of digits, and repeating decimals settle into a repeating block; both of these are rational. So the statement that best reflects irrational numbers is the one describing decimals that do not terminate or repeat.