Which of the following describes irrational numbers?

• A. Pi
• B. the number of decimal points is infinite (Pi or sqrt(5))
• C. They can be written as a ratio of two integers.
• D. All of their decimal representations terminate.

Answer: (B)

Irrational numbers don’t end in their decimal form. Their digits go on forever without settling into a repeating pattern. Saying the decimal expansion has infinitely many digits fits this behavior, and Pi and sqrt(5) are well-known examples. In contrast, being able to write a number as a ratio of two integers describes rational numbers, and having all decimals terminate describes rational numbers too. Simply naming Pi doesn’t describe the whole idea, since many irrationals exist beyond Pi.