Transcript Section 2-1 Numbers & Estimates

Real Numbers
• Real Numbers are all numbers
that can be located on Real
Number line.
• This includes all whole numbers,
all fractions, all decimals, all
roots, etc.
Types of Real Numbers
• There are two types of Real
Numbers
1) Rational Numbers
2) Irrational Numbers
Rational Number
• A Rational Number is any number that
can be written as a RATIO (fraction)
between 2 integers
• Examples of Rational Numbers:
3
1
9
, 3.55 , 2. 6 , 9 , 2 , 5 ,
, 100,
3
4
2 3
• The decimal of a Rational Number is
either terminating or repeating.
Irrational Number
• A number that cannot be written as a ratio
between 2 integers is called an irrational
number
• Examples if Irrational Numbers :
 , 2 , 2.677182793.., etc
• The decimal of an irrational number is
non-terminating and non-repeating
• Radicand – The number or
expression that is under the radical
sign
• In the expression 2
the 2 is called the radicand
Example 1 : Use the calculator to find
the decimal equivalent of each radical
expression. Is the radical a rational or
irrational number?
Round your final answer to the 100ths
place value
a) 5 b) 31 c) 81
2.24
5.57
Irrational
Irrational
9
Rational
• You can never take the square
root of a negative number.
 25  undefined
• Why ?
• Answer: because there is no
number, that when squared will
give you a negative
Rules For Simplifying Radicals
Method 1:
1) Steps
Find the factor tree for the radicand
2) Pull any pairs out of the radical
and leave non pairs under the
radical
3) Multiply pairs and non pairs
Rules For Simplifying Radicals
Method 2:
1) Steps
Find the largest perfect square that
goes into the radicand
2) Write the radicand as a product
of the perfect square and a number\
3) Pull the perfect square out of
the radical
Examples : Use the rules of
simplifying radicals to simplify each
expression
a) 32
b) 300
16  2
100  3
4 2
10 3
Examples : Use the rules of
simplifying radicals to simplify each
expression
a) 125
25 5
5 5
b) 24
46
2 6