Rational and Irrational Numbers

This video tutorial explains the difference between rational and irrational numbers. It defines rational numbers as those that can be expressed as a ratio of two integers, including fractions, integers, and finite decimals. The video also covers repeating decimals and how they can be rational. It then discusses irrational numbers, which cannot be expressed as a ratio of two integers, such as non-repeating decimals, certain square roots, pi, and e. The tutorial provides examples and methods to identify these numbers, helping viewers understand their characteristics and differences.

Which of the following is a rational number?

• 3/4

• e

• Square root of 2

• Pi

How can the number 0.25 be classified?

• Rational number

• Irrational number

• Whole number

• Prime number

Which of the following is a repeating decimal?

• 0.333...

• 0.25

• Square root of 5

• Pi

What is the fraction representation of 0.666...?

• 3/4

• 2/3

• 1/3

• 5/6

Which of the following square roots is a rational number?

• Square root of 2

• Square root of 9

• Square root of 7

• Square root of 3

What is the decimal representation of the square root of 7?

• 1.73205080...

• 1.41421356...

• 3.14159265...

• 2.64575131...

Which of the following numbers is irrational?

• 4/5

• Pi

• 0.75

• 1/2

What is the approximate decimal value of the number e?

• 1.41421

• 1.61803

• 3.14159

• 2.71828

Which of the following is NOT a characteristic of irrational numbers?

• They have an infinite number of decimal places.

• Examples include pi and e.

• They do not repeat.

• They can be expressed as a ratio of two integers.

Which of the following is a characteristic of rational numbers?

• They cannot be expressed as a fraction.

• They are always whole numbers.

• They are always positive.

• They have a finite or repeating decimal expansion.