G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 3 P TE

Homework

Unit 1 · Lesson 3: Rational vs. Irrational Numbers

Objective: I will identify rational and irrational numbers and the difference between them.

Vocabulary Steps:

Squared Numbers (Perfect Square): the result after

multiplying an integer by itself

Rational Numbers: whole numbers, fractions, and decimals

represented as a ratio of two integers; can be represented in

fractional form:

풙풙

풚풚

integers and y ≠ zero.

1.5 =

3

2 =^ ratio^

Irrational Numbers: the set of all numbers that cannot be

written as a ratio of two integers; it cannot be written as a

simple fraction because the decimal is non-terminating and

non-repeating.

0.101101110... , �^23 ,휋휋,√ 10 ,√1.6,−√ 123

1. Determine if the number can be
   expressed as a fraction.
    If so, the number is rational.
   
   
   • Check for terminating or
     repeating decimals.
   
   
   • Look for perfect squares.
      If not, the number is irrational.
   
   
   
   


2. Justify your answer.

Example # 1

Directions: Determine if the given real number is rational or irrational. Justify your answer.

Which of the following is an irrational number and why?

a. 7

b. 10278

c. (^) √ 3
d. 99
Solution:
Irrational; the decimal expansion of this number does not
terminate or repeat.
True or False? 0.333... is an irrational number. Justify your
answer.
Solution:
False; Understand that this is a common rational number
1
3
, expressed in decimal form. Even though the decimal
expansion may seem irrational because it never ends, the
fact that it has a pattern of a repeating digit makes it a
rational number
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