Rational and Irrational Numbers

The video tutorial introduces irrational numbers, explaining their definition and how they differ from rational numbers. It covers the characteristics of irrational numbers, such as non-terminating and non-repeating decimals, and discusses symbols used to represent them, including the dot dot dot, square roots of non-perfect squares, and pi. The tutorial provides examples and practice questions to help recognize irrational numbers, concluding with a summary of key points.

What is the main characteristic of an irrational number?

• It can be expressed as a fraction.

• It is a decimal that terminates.

• It is a decimal that neither terminates nor repeats.

• It is a decimal that repeats.

Which symbol is used to indicate a decimal that continues forever without repeating?

• Exclamation mark (!)

• Dot dot dot (...)

• Question mark (?)

• Asterisk (*)

Which of the following square roots is an irrational number?

• Square root of 5

• Square root of 9

• Square root of 25

• Square root of 16

Why is pi considered an irrational number?

• It is a decimal that repeats.

• It is a decimal that goes on forever without repeating.

• It is a decimal that terminates.

• It can be exactly expressed as a fraction.

Which of the following is a rational approximation of pi?

• 3.142857

• 3.14

• 3.1415926535

• 3.14159

Which of the following numbers is irrational?

• Square root of 7

• 8.2 repeating

• 3.14

• Square root of 9

What makes the square root of 7 an irrational number?

• The square root of 7 is a terminating decimal.

• The square root of 7 is a repeating decimal.

• 7 is a perfect square.

• 7 is not a perfect square.

Which of the following is a rational number?

• Square root of 5

• 3.14

• Pi over 2

• 2 pi

What is the result of the square root of a perfect square?

• An irrational number

• A repeating decimal

• An integer

• A non-terminating decimal

Which of the following uses the dot dot dot notation to indicate it is irrational?

• 3.14

• 8.2 repeating

• Square root of 9

• 3.27512...