Rational and Irrational Numbers

The video explains rational numbers, which are numbers that can be expressed as a fraction of two integers. It covers examples of whole numbers, decimals, and repeating decimals as rational numbers. The video also discusses zero as a rational number and explains why certain square roots are irrational. The key takeaway is that rational numbers can be written as fractions of integers, and their decimal forms either terminate or repeat.

What is a rational number?

• A number that is always negative.

• A number that is always positive.

• A number that cannot be expressed as a fraction.

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

Which of the following is a rational number?

• The square root of 2

• The square root of 3

• 0.333... (repeating)

• Pi (π)

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

• 1/6

• 0/6

• 6/1

• 6/0

Why is zero considered a rational number?

• Because it is a positive number.

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

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

• Because it is a negative number.

Which of the following decimals is a rational number?

• The square root of 5

• 0.123456789...

• 0.75

• Pi (π)

How can a repeating decimal like 0.333... be expressed as a fraction?

• 1/3

• 3/10

• 1/10

• 3/1

What is the fraction form of 0.18 repeating?

• 18/10

• 1/18

• 18/99

• 18/100

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

• The square root of 16

• The square root of 4

• The square root of 9

• The square root of 3

Why is the square root of 3 considered irrational?

• Because its decimal form neither terminates nor repeats.

• Because its decimal form repeats.

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

• Because its decimal form terminates.

What is a characteristic of irrational numbers?

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

• Their decimal form either terminates or repeats.

• They are always whole numbers.

• Their decimal form neither terminates nor repeats.