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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 … … … … 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 Answer: If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

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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 Answer: If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

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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 Answer: If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

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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 Answer: If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

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The set of real numbers can be divided into two sets: RATIONAL NUMBERS IRRATIONAL NUMBERS and Numbers that can be written in the form a. b Numbers that can be written in the form a. b Numbers that cannot 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 integers all fractions 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? 10 cm x cm 24 cm Using Pythagoras Answer: x is rational

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4 Is x rational or irrational for this triangle? 4 cm x cm 12 cm Using Pythagoras Answer: x is irrational

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