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RATIONAL AND IRRATIONAL NUMBERS
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Recurring decimals
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Recurring decimals contain digits that are repeated over and over again.
… … … … are all examples of recurring decimals Dots are used to show how the decimals recur.
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Changing recurring decimals to fractions
1 Change to a fraction. let multiply both sides of the equation by 10 write underneath subtract the two equations divide both sides by 9 If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000. Answer:
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Changing recurring decimals to fractions
2 Change to a fraction. let multiply both sides of the equation by 100 write underneath subtract the two equations divide both sides by 99 If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000. Answer:
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Changing recurring decimals to fractions
3 Change to a fraction. let multiply both sides of the equation by 1000 write underneath subtract the two equations divide both sides by 999 If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000. Answer:
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Changing recurring decimals to fractions
4 Change to a fraction. let multiply both sides of the equation by 100 write underneath subtract the two equations divide both sides by 99 If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000. Answer:
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The set of real numbers can be divided into two sets:
RATIONAL NUMBERS and IRRATIONAL NUMBERS Numbers that can be written in the form a . b Numbers that cannot be written in the form a . b
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Rational numbers include:
all fractions all integers all mixed numbers all terminating decimals all recurring decimals some square roots some cube roots
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Irrational numbers include:
some square roots some cube roots some trig ratios
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1 Which of these numbers are irrational numbers?
Answer: and
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2 Write each of these numbers in the correct place on the Venn diagram.
Rational numbers Integers
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3 Is x rational or irrational for this triangle?
x cm 10 cm 24 cm Using Pythagoras Answer: x is rational
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4 Is x rational or irrational for this triangle?
12 cm 4 cm x cm Using Pythagoras Answer: x is irrational
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