Exploring Rational and Irrational Numbers

The video provides an introduction to rational and irrational numbers. Rational numbers are defined as numbers that can be expressed as a fraction of two integers, including terminating and repeating decimals. Examples include whole numbers, negative numbers, and fractions. Irrational numbers, on the other hand, cannot be expressed as a fraction of two integers and include non-repeating, non-terminating decimals such as the square root of non-perfect squares, pi, and e. The video offers examples and explanations to help understand these concepts.

What defines a number as rational?

• A number that cannot be expressed as a fraction

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

• A number with a decimal that never ends or repeats

• A number that is a perfect square

Can whole numbers be considered rational?

• No, because they do not have decimals

• Yes, if they are positive

• Yes, because they can be expressed as fractions

• No, because they are not fractions

Is the number 0 considered rational?

• No, because it is not a positive number

• No, because it does not have a decimal form

• Yes, but only in certain contexts

• Yes, because it can be expressed as 0/1

Can terminating decimals be considered rational numbers?

• No, because they do not repeat

• Yes, because they can be expressed as fractions

• Yes, but only if they are negative

• No, because they cannot be written as fractions

How can a repeating decimal be classified?

• As an undefined number

• As a rational number

• As a non-integer

• As an irrational number

What is an example of an irrational number?

• The square root of 25

• 0.333...

• 8 over 10

• The square root of 3

What makes a number irrational?

• If it can be written as a fraction of two integers

• If its decimal form terminates

• If its decimal form neither terminates nor repeats

• If it is a negative number

Why is Pi considered an irrational number?

• Because its decimal form never ends or repeats

• Because it is a repeating decimal

• Because it can be expressed as a fraction

• Because it is used in geometry

Which of the following is a rational number?

• The square root of 2

• The cube root of 30

• -63

• Pi

What is the square root of 49 classified as?

• Rational, because it is a perfect square

• Irrational, because it is a square root

• Irrational, because it cannot be expressed as a fraction

• Rational, because it is a terminating decimal