Download Lesson 4: Rational and Irrational Numbers

Lesson 4: Rational and Irrational Numbers
Specific Outcomes:
- Sort a set of numbers into rational and irrational numbers (2.1).
- Determine an approximate value of a given irrational number (2.2).
- Approximate the locations of irrational numbers on a number line, using a variety of
strategies, and explain the reasoning (2.3).
- Order a set of irrational numbers on a number line (2.4).
Investigation with decimals:
Use your calculator to convert the following,
a)
b)
29
11
29
8
to a decimal
What do you notice about this decimal?
to a decimal
What do you notice about this decimal?
Definitions:
29
Repeating decimals: Decimals that have a recurring pattern of digits. e.g., 11 = 2.6363
Non-repeating decimals: Decimals that have no recurring pattern of digits.
47
e.g., 26 = 1.807692308
Terminating decimals: Decimals with a finite number of digits. e.g.,
29
8
= 3.625
29
Non-terminating decimals: decimals with an infinite number of digits. e.g., 11 = 2.6363
Example 1: State whether the decimal equivalent of each number repeating/nonrepeating and whether it is terminating/non-terminating.
a)
11
9
b) √8
c)
13
26
d) √0.16
Definition of rational numbers:
𝑚
- Any number that can be written in the form 𝑛 , n ≠ 0 where m and n are integers.
-
Any decimal that is terminating or repeating.
Can be converted into a fraction.
-
e.g., 11 = 2.636363…, 0.45, √25 = 5
29
Definition of irrational numbers:
𝑚
- A number that cannot be written in the form 𝑛
-
Any decimal that is non-terminating and non-repeating
Cannot be converted into a fraction
e.g., π, √5 = 2.236…
Example 2: Identify each number as rational or irrational and state why.
a) 0.625
b) 2.145145…
c) 1.21
d) √7
3
e) √−30
f)
−29
19
Example 3: Use a number line to order these numbers from least to greatest.
3
3
4
√13, √18, √9, √27, √−5
Example 4: Use a number line to order these numbers from least to greatest.
3
3
4
√2, √−2, √6, √11, √30
Example 5: Determine whether the perimeter of each square is a rational number or an
irrational number.
a) A square with area 36 cm2
b) A square with area 35 cm2
Practice Questions: Page 211 # 3, 5, 6, 9, 10, 12, 20