Download Irrational numbers

Irrational numbers
Briana was doing her homework
but her pen popped
and ink went all over her work.
Her teacher can see she had
completed the work
so asks her to explain what she did.
Write down what Briana would
say to her teacher to
explain her understanding.
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Irrational numbers
These rational decimals have been converted to fractions but are jumbled up.
Can you match the correct decimal to the correct fraction without using a
calculator?
0.4
0.45
0.432
0.409
0.428571
0.461538
3
/7
9
/22
6
/13
4
/9
5
/11
16
/37
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Irrational numbers
These rational decimals have been converted to fractions but are jumbled up.
Can you match the correct decimal to the correct fraction without using a
calculator?
0.4
0.45
0.432
0.409
0.428571
0.461538
3
/7
9
/22
6
/13
4
/9
5
16
/11
/37
4
/9
5
/11
16
/37
9
/22
3
/7
6
/13
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Irrational numbers
Understanding irrational numbers
If 12 = 1
Then what does √1 equal?
What about √4?
√36?
If the square root of a number is an integer then it is a perfect square.
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Irrational numbers
What about √2?
It's not an integer.
It's not a terminating decimal.
It's not a repeating decimal.
Because it does none of the above it is an irrational number.
What about -√2?
What other irrational numbers can you think of?
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Irrational numbers
Decide whether each of the following numbers is rational or
irrational.
If it is rational, explain how you know.
A
B
C
D
E
F
G
0.333
√4
√2
π = 3.141592..
11
1
/7 = 0.142857
12.3456565656
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Irrational numbers
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Irrational numbers
√5 lies between which two perfect squares?
√7
√6
√5
√4
√9
√8
3
2
√48 lies between which two perfect squares?
√36
√37
√38
√39
√40
√41
√42
√43
√44
√45
√46
√47
48
√48
√
√49
6
7
Decide which perfect squares these square roots lie between.
√5
√8
√11
√58
√86
√109
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Irrational numbers
Which of the following numbers are irrational?
Estimate where they will lie on a number line.
4.7
6
√47
4
2π
5¼
5
4.7
5¼
7
6
5
4
2π
6
7
6
√47
Working in pairs decide where the rational and irrational numbers
would lie on a number line.
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Irrational numbers
A
3/7
√8
4
4.06
5.6
B
5/7
√2
2.05
3
7.0
C
2/5
√5
2.61
4.3
9
D
1.04
1.4
22/3
√10
5
E
4
1
√3
2.5
8.82
F
-3/4
2.6
√15
5.2
6
G
√7
4½
8.5
8.53
9
H
2/3
1.4
√13
7
8.83
I
-7/10
2
2.0
2.07
√11
J
12
√ /3
√6
4
5.5
6.3
/9
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Irrational numbers
K
-√7
2/5
0.95
1
½π
√4
L
4/9
√3
√9.3
π
7.92
8
M
-4π
√0.3
√2
3
3.86
9/2
N
-√3
2/3
√9.6
2π
7.73
9
O
-7/10
√1.2
√π
√4
3.46
7
P
-√3.4
√π
√12/3
2.14
√5
7
Q
-(2xπ)
-√0.2
√3
R
5/7
√2
√2.6
S
-π
0.6
√3
T
- 3 /4
¼π
2
23/7
4.24
5
3.43
3π
10
√6.4
8
/3
7
√9.0
√19
6.14
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Irrational numbers
Without using your calculator, label approximate locations for the following numbers on the number line.
a)
b)
c)
d)
π
-(½ x π)
2√2
√17
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Irrational numbers
Without using your calculator, label approximate locations for the following numbers on the number line.
a)
b)
c)
d)
π
-(½ x π)
2√2
√17
-(½ x π)
π
a
b
c
2√2
d
√17
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Irrational numbers
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Irrational numbers
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Irrational numbers
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Irrational numbers
Math Homework
Answer questions from the textbook:
Page 477
Exercise 3-15
Page 478
Ex 34, 36, 38, 40
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