Irrational Numbers Example Problem

The video tutorial explains the concept of irrational numbers, distinguishing them from rational numbers. It highlights that irrational numbers cannot be expressed as fractions or terminating decimals. Using examples like pi, the video illustrates that irrational numbers are infinite and continue indefinitely. The tutorial concludes that there are infinitely many irrational numbers between any two numbers, such as 1 and 6.

What is the main difference between irrational numbers and whole numbers?

• Whole numbers are non-terminating decimals.

• Irrational numbers cannot be expressed as simple fractions.

• Irrational numbers can be expressed as fractions.

• Whole numbers are always negative.

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

• 0.5

• Square root of 2

• Pi (π)

• e (Euler's number)

Why is pi considered an irrational number?

• It is less than 3.

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

• It is a whole number.

• It can be expressed as a fraction.

How many irrational numbers exist between 1 and 6?

• None

• One

• Infinitely many

• A finite number

Which statement is true about irrational numbers?

• They can be expressed as a simple fraction.

• They are always greater than 10.

• They are non-terminating and non-repeating.

• They have a repeating decimal pattern.