Classifying Rational Numbers

Classifying Rational Numbers

By Marissa Baker

​Classifying Real Numbers

1. Real Numbers include all rational and irrational numbers.

2. A real number represents a value on the number line.

3. All rational numbers can be written as the ratio of two integers. ​

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Numbers that can be expressed in the form of a/b; where a and b are integers and b does not equal zero.

Whole Numbers

All whole numbers greater than zero.

​Natural Numbers

Vocabulary

Integers

The set of whole Numbers and their opposites.

The numbers starting with zero.

​Rational Numbers

Real Numbers

The set of numbers that includes all rational numbers and irrational numbers.

4. Some other examples of rational numbers are the

   1. square root of any perfect square,

   2. terminating and repeating decimals,

   3. and fractions.

5. All irrational numbers cannot be written as the ratio of two integers.

6. The square root of any whole number that is not a perfect square is irrational.

7. Non-terminating and non-repeating decimals are irrational.

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Complete the inside of the foldable. Use slide 4 as reference if needed.

Practice

Review questions on the paper prior to completing the questions on the following slides.

​​Assessment

Multiple Choice

Which subset of real numbers is defined as the set of whole numbers and their opposites?

• Natural

• Integers

• Rational

• Irrational

Multiple Choice

Fill in the blank:

All rational numbers can be written as the ____ of two integers.

• Sum

• Difference

• Product

• Ratio

Multiple Choice

What is the most specific classification for the following number: 19

• Natural

• Whole

• Integer

• Rational

Multiple Choice

Determine whether the following statement is true or false and the correct reasoning.

-2 is a whole number

• True; it can be written as a ratio of two numbers

• True; it is a counting number

• False; it is the opposite of 2 which makes it an integer

• False; it is a negative so it must be irrational

Multiple Choice

Which of the following numbers is irrational?

• $$-\ \sqrt[]{9}$$  

• $$1.333333333...$$  

• $$\left(\sqrt[]{\pi}\right)^2$$  

• $$-\ \frac{3}{4}$$  

Multiple Select

Determine all the correct subsets for the number below:

0

• Natural

• Whole

• Integers

• Rational

• Irrational

Open Ended

Emily classifies $$\sqrt[]{64}$$  as an irrational number since there is a square root. Robert claims $$\sqrt[]{64}$$  is an integer. Who is correct? Explain your reasoning.