Understanding Rational and Irrational Numbers

The video tutorial by Mr. J explains the concept of irrational numbers, which cannot be expressed as a fraction of two integers and have non-terminating, non-repeating decimal forms. The video begins with a recap of rational numbers, which can be expressed as fractions and have terminating or repeating decimals. It then provides examples of irrational numbers, such as the square root of non-perfect squares, Pi, and Euler's number. The tutorial concludes with exercises to determine whether given numbers are rational or irrational.

What is a characteristic of a rational number?

• It cannot be expressed as a fraction of two integers.

• It is always a whole number.

• Its decimal form neither terminates nor repeats.

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

Which of the following is an example of a rational number?

• Pi

• 0.2 repeating

• Square root of 2

• Euler's number

Why is the square root of 2 considered irrational?

• Its decimal form repeats.

• Its decimal form terminates.

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

• Its decimal form neither terminates nor repeats.

Which of the following numbers is irrational?

• Square root of 49

• 3.14

• Pi

• 9/10

What is Euler's number approximately equal to?

• 1.618

• 2.718

• 1.414

• 3.14

How can -63 be classified?

• Irrational

• Both

• Rational

• Neither

What is the nature of the number 31723.31723...?

• Integer

• Rational

• Irrational

• Whole number

What is the square root of 49?

• 7

• 49

• Irrational

• 0

Which of the following is a repeating decimal?

• Euler's number

• 8.71425

• 3.14159

• Square root of 50

Why is the square root of 50 considered irrational?

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

• Its decimal form terminates.

• Its decimal form neither terminates nor repeats.

• It is a perfect square.