Understanding Rational and Irrational Numbers

The video tutorial explains the difference between rational and irrational numbers, providing definitions and examples. Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot. The tutorial includes examples to identify these numbers, discusses the irrational side lengths of squares, and examines rational approximations of pi. A final practice problem helps reinforce the concepts.

Which of the following is a characteristic of a rational number?

• It can be expressed as a fraction of two integers.

• It cannot be expressed as a fraction.

• It has a decimal that never repeats.

• It includes the number pi.

What makes the number 0.01324 irrational?

• It is a repeating decimal.

• It is a terminating decimal.

• It is a fraction.

• It is a non-repeating, non-terminating decimal.

Why is the square root of 20 considered irrational?

• 20 is not a perfect square.

• The square root of 20 is a repeating decimal.

• The square root of 20 is a terminating decimal.

• 20 is a perfect square.

Which of the following is a rational approximation of pi?

• A non-terminating decimal

• The square root of 2

• 3.14

• The symbol pi itself

Which of the following numbers is rational?

• The square root of 50

• 3.14159

• Pi

• A non-repeating decimal