Which of the following types of numbers are irrational? (Select all that apply.) A. Repeating decimals B. π (pi) C. Negative integers D. Decimals that go on forever without repeating

Answer 1

Irrational numbers are those that cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal representations.

Let's evaluate the options:

A. Repeating decimals - These are rational numbers because they can be expressed as a fraction. (Not irrational)

B. π (pi) - This is a well-known irrational number as it cannot be expressed as a fraction of two integers. (Irrational)

C. Negative integers - These are rational numbers because they can be expressed as a fraction (e.g., -2 can be written as -2/1). (Not irrational)

D. Decimals that go on forever without repeating - These are irrational numbers. (Irrational)

So, the irrational numbers from the options are: B. π (pi) and D. Decimals that go on forever without repeating.