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Real Numbers
Week 1 Topic 1
Real Numbers



Irrational Numbers
 Numbers that cannot be written as a fraction
 √2, π
Rational Numbers
 Numbers that can be written as a fraction
 Decimals that repeat
 Decimals that stop
 √25, ½, 5, 0.123, 0.333333…
Real Numbers
 Set of all irrational and rational numbers
Real Numbers
 Integers
 Positive and negative counting numbers
(plus 0)
 {…-3, -2, -1, 0, 1, 2, 3…)
 Whole Numbers
 Counting numbers starting at 0
 {0, 1, 2, 3…}
 Natural Numbers
 Counting numbers starting at 1
 {1, 2, 3…}
Real Numbers
 Infinite sets- not countable
 Whole numbers greater than 8
 {3, 4, 5 …}
 Finite sets- countable
 Integers between 2 and 17
 {2, 5, 7, 19, 23}
Real Numbers
 Estimating the value of an irrational
number
 Compare perfect square values
 List perfect squares close to your value
√67
√49 = 7; √64 = 8; √81 = 9
67 is between 64 and 81 so √67 is between 8
and 9
8 < √67 < 9
Real Numbers
1. Which of the following represents an
infinite set of numbers?
a.
b.
c.
d.
{1/2, 1/3, ¼, 1/5}
{Negative integers}
{-3, -1, 0, 1, 3}
{Natural numbers between 5 and 20}
Real Numbers
1. Which of the following represents an infinite set of
numbers?
a. {1/2, 1/3, ¼, 1/5}
This set has a clear start and stop, we see exactly 4
values in the set so it is countable or finite
b. {Negative integers}
integers go off to infinite so this set is not countable
c. {-3, -1, 0, 1, 3}
We can count the 5 values in this set.
d. {Natural numbers between 5 and 20}
We can list and count the values in this set. 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
Real Numbers
2. Which of the following is an irrational
number?
a. √5
b. √9
c. 7
d. 3.78
Real Numbers
2. Which of the following is an irrational
number?
a. √5
b. √9 = 3 whole numbers are rational
c. 7 = 7/1 whole numbers are rational
d. 3.78 = 378/100 decimals that stop are
rational
Real Numbers
3. Between which two consecutive integers
is √113 ?
a. 12 and 13
b. 8 and 9
c. 10 and 11
d. 11 and 12
Real Numbers
3. Between which two consecutive integers
is √113 ?
a. 12 and 13
b. 8 and 9
c. 10 and 11
d. 11 and 12
82 = 64; 92 = 81; 102 = 100; 112 = 121; 122
= 144; 132 = 169