Rational and Irrational Numbers

The video tutorial explains the difference between rational and irrational numbers. Rational numbers can be expressed as the ratio of two integers, including repeating and terminating decimals. The video demonstrates converting repeating decimals to fractions using algebra. It also covers identifying irrational numbers, such as the square root of a prime number, and provides examples like pi and e. Terminating decimals are shown to be rational, and the video concludes with examples of irrational numbers.

What is a rational number?

• A number that cannot be expressed as a fraction.

• A number that is always positive.

• A number that can be expressed as a fraction of two integers.

• A number that is always negative.

Which of the following numbers is rational?

• 194

• e

• Square root of 11

• Pi (π)

Which of the following is a characteristic of a repeating decimal?

• It can be expressed as a fraction.

• It is always irrational.

• It never ends.

• It is always negative.

What is the decimal representation of 2/3?

• 0.25

• 0.666...

• 0.5

• 0.75

How can a repeating decimal be converted into a fraction?

• By rounding the decimal.

• By using algebraic methods.

• By using a calculator.

• By guessing the fraction.

What is the result of dividing 2 by 3?

• 2.0

• 1.5

• 0.5

• 0.666...

What makes the square root of a prime number irrational?

• It is always negative.

• It is always a whole number.

• It can be expressed as a fraction.

• It results in a non-terminating, non-repeating decimal.

Which of the following is an example of an irrational number?

• Pi (π)

• 1.5

• 3/4

• 0.25

Which of the following is a terminating decimal?

• Square root of 2

• Pi (π)

• 1.09

• e

What is the nature of the number pi (π)?

• It is irrational.

• It is rational.

• It is a whole number.

• It is a negative number.