Unveiling the Number System: Rational and Irrational Numbers

1
The Number System
Rational and Irrational Numbers
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Learning Outcomes
1 Understand the difference between rational
and irrational numbers
2
Approximate the value of irrational numbers
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Rational and Irrational Numbers
Rational numbers A number is rational if it can
be expressed as a fraction. It includes
positive and negative numbers including 0.
Irrational numbers Irrational numbers cannot be
expressed as a simple fraction. When written as
a decimal, they are non recurring and do not
terminate.
_
.
-
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Approximating Irrational Numbers
Approximate the value of v6
v6
v9
v4
2 2.4 3 By looking at consecutive square numbers
close to v6, you can estimate its value to be
between 2 and 3.
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Approximating Irrational Numbers
Approximate the value of v6 to the nearest
hundredth
v6
6.25
5.76
2.4
2.5
2.4
2.5
2.45
2.42
2.5 2
9 6
1 2 5
4 8 0
5 0 0
5 7 6
6 2 5
Squaring both numbers shows that v6 is
approximately half way between 2.4 and 2.5,
therefore a reasonable estimate to the nearest
hundredth would be 2.45.
5.76
6.25
Square 2.5 to see how close it is to 6.
Square the estimate of 2.4 to see how close it
is to 6.
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Practice Questions
1
Locate the two integers which v5 lies between.
Which letter on the number line best represents
the value of v7 ?
2
A
B
C
3
2
Which is the best estimate for the value of v7
to the nearest tenth ?
3
2.8
2.7
2.6
A
C
B
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Solutions
1
Locate the two integers which v5 lies between. 2
and 3
Which letter on the number line best represents
the value of v7 ? B Which is the best estimate
for the value of v7 to the nearest tenth ?
2
A
B
C
3
2
3
2.8
2.7
2.6
A
C
B
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Challenge
1
Which is the best estimate for the value of v82 to
the nearest hundredth?
9.06
9.05
9.10
A
C
B
Write down the approximate value of 2p to the
2
nearest hundredth?
Write down the approximate value of 2v3 to the
3
nearest hundredth?
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Solutions
1
Which is the best estimate for the value of v82 to
the nearest hundredth?
9.06
9.05
9.10
A
C
B
Write down the approximate value of 2p to the
2
nearest hundredth?
6.28
Write down the approximate value of 2v3 to the
nearest hundredth? 3.46
3
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