Understanding Rational and Irrational Numbers

The video tutorial explains the classification of numbers into rational and irrational categories. Rational numbers can be expressed as fractions and have either terminating or repeating decimals. Examples include integers and fractions like 0.4 and 0.3 repeating. Irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimals, such as the square root of 5 and pi. The tutorial also covers additional number sets like integers and whole numbers, and provides examples to illustrate the concepts, including the cube root of 27 and the square root of 81.

What is a characteristic of rational numbers?

• Their decimal form is non-terminating and non-repeating.

• They cannot be expressed as a fraction.

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

• They are always whole numbers.

Which of the following is a rational number?

• Pi

• Square root of 5

• 0.333... (repeating)

• Square root of 2

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CCSS.8.NS.A.1

Why is pi considered an irrational number?

• Its decimal form is non-terminating and non-repeating.

• It is a whole number.

• Its decimal form terminates.

• It can be expressed as a fraction.

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CCSS.8.EE.A.2

What is the cube root of 27?

• 3

• 81

• 27

• 9

How can 5.9 be expressed as a fraction?

• 59/100

• 9/5

• 5/9

• 59/10

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CCSS.7.NS.A.2D

CCSS.8.NS.A.1

What is the decimal representation of 1/3?

• 0.3333

• 0.333... (repeating)

• 0.33

• 0.3

Which of the following numbers is rational?

• Cube root of 27

• Square root of 5

• Square root of 27

• Pi

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CCSS.8.NS.A.1

Which of the following numbers is irrational?

• 0.4

• 5.9

• Cube root of 16

• Square root of 81

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CCSS.6.EE.A.1

Which of the following is a perfect square?

• 5

• 16

• 81

• 27

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CCSS.8.EE.A.2

What is the cube root of 16 approximately?

• 3.2

• 3.0

• 2.7

• 2.5

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CCSS.8.EE.A.2