Name:________________________________________________ Class Period:________________
Learning Target: We are learning to distinguish between rational and irrational
numbers
The Real Number System:
The set of rational and irrational numbers all together.
Wait….There are numbers that aren’t real????
*Ask Siri….What is 20 divided by zero?
Try putting the following numbers in your calculator:
√−10
20
0
For 8th grade math, we will focus on the sets of rational and irrational numbers.

If I told you that saving money, studying for a test, and going to bed at a reasonable hour were all rational
decisions, what do you think rational means?

If I told you that spending your lifesavings on candy, yelling at everyone, and jumping out of a plane were all
irrational decisions, what do you think irrational means?

Work with your group. Which numbers do you think are rational and which numbers do you think are
irrational? Make sure everyone in your group agrees.
Rational Numbers
1. Whole numbers, integers, and zero.
Both (Rational
and Irrational)
Can be positive
or negative
Irrational Numbers
1. Special numbers like 𝜋
2. Terminating or repeating decimals
2. Non-terminating, non-repeating decimals
3. ALL fractions with a denominator that
is not zero
3.
Cannot be written as a fraction
4.
Non-perfect squares
4.
Perfect squares
Let’s Try a few!
482
57
3
0
√18
-√25
−23
𝜋
0.131331333 …
̅̅̅
0. ̅63
√24
−√16
-19
̅̅̅
−1. ̅82
15
0
2
3
5
Practice: Classify each number as rational or irrational. Justify your selection using one of the characteristics.
Number
R or I?
Justify
Number
R or I?
√4
0.895210351….
-27.5
−0.2857
√37
√64
1
9
−15
−
0.09
√7
̅̅̅̅
-100.66
Justify