Understanding Rational and Irrational Numbers

The video tutorial explains the concept of rational numbers, which are numbers that can be expressed as the ratio of two integers. It provides examples of rational numbers, such as 0.3737 and 12/31, and explains how to identify them. The tutorial also covers irrational numbers, like the square root of 11, and explains why they cannot be expressed as a ratio of two integers. Additionally, it discusses how decimals, whether terminating or repeating, can be converted into rational numbers. Finally, the video explores the result of combining rational and irrational numbers, highlighting that such combinations are irrational.

What does it mean for a number to be rational?

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

• It is a whole number.

• It cannot be expressed as a fraction.

• It is a decimal number.

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CCSS.8.NS.A.1

Which of the following is a rational number?

• Pi

• Square root of 11

• Square root of 2

• 0.3737

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CCSS.8.NS.A.1

Why is the square root of 11 considered irrational?

• Because it is a whole number.

• Because it is a repeating decimal.

• Because it can be expressed as a fraction.

• Because 11 is not a perfect square.

Which of these numbers is not rational?

• 12/31

• 0.44444

• 0.3737

• Square root of 11

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CCSS.8.NS.A.1

Which of the following is a characteristic of irrational numbers?

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

• They are always repeating decimals.

• They are always whole numbers.

• They cannot be expressed as a fraction of two integers.

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CCSS.7.NS.A.2D

CCSS.8.NS.A.1

What characteristic makes a decimal number rational?

• It is either terminating or repeating.

• It is a whole number.

• It is a non-repeating decimal.

• It is an irrational number.

Which of the following is a rational number?

• Square root of 8

• 0.44444

• Pi

• e

How can 0.44444 be expressed as a fraction?

• 444/1,000

• 4/10

• 44/100

• 444,444/1,000,000

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CCSS.HSN.RN.B.3

What happens when you add a rational number to an irrational number?

• The result is irrational.

• The result is rational.

• The result is a repeating decimal.

• The result is a whole number.

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CCSS.7.NS.A.1D

Which of the following expressions is irrational?

• 2 + square root of 8

• 4/2

• 0.5

• 2 + 3

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CCSS.7.NS.A.1D