Delve into the fascinating realm of the number system as we explore the distinction between rational and irrational numbers. Discover the beauty and intricacy behind these mathematical entities and how they play a fundamental role in our understanding of the world. Unravel the properties and characteristics that define rational numbers, which can be expressed as fractions, and uncover the enigmatic nature of irrational numbers, whose decimal representations are infinite and non-repeating. Join us on this captivating journey as we unlock the secrets of the number system and deepen our appreciation for the mathematical wonders that surround us. Delve into the fascinating realm of the number system as we explore the distinction between rational and irrational numbers. Discover the beauty and intricacy behind these mathematical entities and how they play a fundamental role in our understanding of the world. Unravel the properties and characteristics that define rational numbers, which can be expressed as fractions, and uncover the enigmatic nature of irrational numbers, whose decimal representations are infinite and non-repeating. Join us on this captivating journey as we unlock the secrets of the number system and deepen our appreciation for the mathematical wonders that surround us.
Unveiling the Number System: Rational and Irrational Numbers
The Number
System
Rational and
Irrational
Numbers
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Learning
Outcomes
1 2
Understand the
difference between Approximate the value
rational and of irrational numbers
irrational numbers
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Rational and Irrational
Numbers
Rational numbers Irrational numbers
A number is rational if it Irrational numbers cannot
can be expressed as a be expressed as a simple
fraction. It includes fraction. When written as
positive and negative_ a decimal, they are non numbers including 0. recurring and do not
terminate.
- .
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Approximating Irrational
Numbers
Approximate the value of
√6
√ √ √9
4 6
2 ≈2.4 3
By looking at consecutive square numbers close to √6, you can
estimate its value to be between 2 and 3.
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Approximating Irrational
Numbers
Approximate the value of √6 to the nearest hundredth
2. 2. 5.7 √ 6.2
4 5 6 5
× × 6
2.49 21.5 2 2.4 ≈ 2.4 2.5
2 2
4 68 5 0 5
50 7 60 2
6 5 Squaring both numbers
= = shows that √6 is
5.76 6.25
approximately half way
Square the estimate of Square 2.5 to see between 2.4 and 2.5,
2.4 to see how close it how close it is therefore a reasonable
is to 6. to 6. estimate to the nearest
hundredth would be 2.45.
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Practice
Questions
1 Locate the two integers which √5 lies
between.
2 Which letter on the number
line best represents the value A B C
2 3
of √7 ?
3 Which is the best estimate for A 2.6 B 2.8 C 2.7
the value of √7 to the nearest
tenth ?
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Solution
s
1 Locate the two integers which √5 lies between. 2 and
3
2 Which letter on the number
line best represents the value A B C
2 3
of √7 ?
3 B A 2.6 B 2.8 C 2.7
Which is the best estimate for
the value of √7 to the nearest
tenth ? WWW.SUDO24.COM
Challeng
e
1 Which is the best estimate for the value of √82
ttohe nearest A 9.10 B 9.06 C 9.05
hundredth?
2 Write down the approximate value of 2π
tnoe atrheest hundredth?
3 Write down the approximate value of 2√3 to
tnheearest hundredth?
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Solution
s
1 Which is the best estimate for the value of √82
ttohe nearest A 9.10 B 9.06 C 9.05
hundredth?
2 Write down the approximate value of 2π
tnoe atrheest hundredth? 6.2
8
3 Write down the approximate value of 2√3 to
the nearest hundredth?
3.46
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