Transcript File

3-7 Before the Bell
Each square root is between two integers.
Name the two integers.
1.
119
10 and 11
2. – 15
–4 and –3
Use a calculator to find each value.
Round to the nearest tenth.
3.
4. –
2
1.4
123
–11.1
3-7
Today’s learning
Target:
I can
• Classify (name) numbers
• Determine if a number is rational or
irrational.
3-7
Vocabulary
Real Numbers:
Natural Numbers
Whole Numbers
Integers
Rational number
Irrational number
1, 2, 3, 4, 5…
0, 1, 2, 3, 4, 5…
… -3, -2, -1, 0, 1, 2, 3, 4, 5…
- any number that can be written
as a ratio (or fraction)
- They never end or repeat.
Recall that rational numbers can be written as
fractions. Rational numbers can also be written
as decimals that either terminate or repeat.
3
4
= 3.8
5
2
= 0.6
3
1.44 = 1.2
3-7
Vocabulary
The set of real numbers consists of the set of
rational numbers and the set of irrational numbers.
3-7
I’ll show you.
Write all names that apply to each number.
1.
5 is a whole number that is
not a perfect square.
irrational, real
5
2. –12.75 –12.75 is a terminating decimal.
rational, real
3.
16
2
16
4
=
=2
2
2
Natural, whole, integer, rational, real
3-7
Try this with a partner.
Write all names that apply to each number.
4.
9
9
=3
Natural, whole, integer, rational,
real
5.
6.
–35.9
–35.9 is a terminating decimal.
rational, real
81
81
9
=
=3
3
3
3
natural, whole, integer, rational,
real
3-7
I’ll show you.
State if each number is rational, irrational,
or not a real number.
7.
21
irrational
8.
0
3
rational
0
=0
3
3-7
Try this with a partner.
State if each number is rational, irrational,
or not a real number.
9.
–4
not a real number
10.
4
9
rational
2
3
3-7
State if each number is rational, irrational,
or not a real number.
11.
23
23 is a whole number that
is not a perfect square.
irrational
12.
9
0
undefined, so not a real number
The Density Property of real numbers
states that between any two real
numbers is another real number. This
property is also true for rational
numbers, but not for whole numbers or
integers. For instance, there is no integer
between –2 and –3.
Additional Example 3: Applying the Density Property
of Real Numbers
2
3
Find a real number between 3
and 3 .
5
5
There are many solutions. One solution is
halfway between the two numbers. To find it,
add the numbers and divide by 2.
2
3
5
1
3
+3
÷2 =6
÷2 =7÷2=3
5
5
5
2
3
1
2
3
4
3 5 3 5 13 5 35
4
32
3
2
1
A real number between 3
and 3
is 3 .
5
5
2
3-7 Did you master today’s learning target?
Lesson Quiz
Write all names that apply to each number.
1.
2
2. – 16
2
real, integer, rational
real, irrational
State if each number is rational, irrational, or
not a real number.
3. 25
0
not a real number
4.
4 •
rational
9
3-7
Assignment:
Lesson 3-7
Page 125, problems 31-47, 57