Rational and Irrational Numbers

The video explains rational numbers, which can be expressed as fractions of two integers. It covers examples of whole numbers, decimals, and repeating decimals as rational numbers. The video also discusses the concept of irrational numbers, using square roots as examples. Key points include the requirement for both numerator and denominator to be integers and the exclusion of zero in the denominator. The video concludes with a summary of rational numbers and their properties.

What is a rational number?

• A number that cannot be expressed as a fraction.

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

• A number that is always negative.

• A number that is always positive.

Which of the following is a characteristic of rational numbers?

• They can only be positive.

• They must have a denominator of zero.

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

• They cannot be decimals.

How can the number 6 be expressed as a rational number?

• 6 over 0

• 6 over 1

• 6 over 6

• 6 over 12

Is the decimal 0.7 a rational number?

• No, because it is a decimal.

• Yes, because it is a terminating decimal.

• Yes, because it is a repeating decimal.

• No, because it cannot be expressed as a fraction.

Why is zero considered a rational number?

• Because it can be expressed as a fraction of two integers.

• Because it is a positive number.

• Because it is a negative number.

• Because it can be expressed as a fraction with zero in the denominator.

What makes a repeating decimal a rational number?

• It is always greater than one.

• It has a pattern that repeats indefinitely.

• It is always less than zero.

• It cannot be expressed as a fraction.

Which of the following is an example of a repeating decimal?

• 0.5

• 0.333...

• 0.25

• 0.75

What is the square root of 25 considered?

• A non-repeating decimal

• A rational number

• An irrational number

• A negative number

Why is the square root of 3 not a rational number?

• Because it is a perfect square.

• Because it is a whole number.

• Because its decimal form does not terminate or repeat.

• Because it can be expressed as a fraction of two integers.

What is an irrational number?

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

• A number that is always positive.

• A number whose decimal form terminates.

• A number whose decimal form neither terminates nor repeats.