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RATIONAL AND IRRATIONAL NUMBERS. Recurring decimals.

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Presentation on theme: "RATIONAL AND IRRATIONAL NUMBERS. Recurring decimals."— Presentation transcript:

1 RATIONAL AND IRRATIONAL NUMBERS

2 Recurring decimals

3 Recurring decimals contain digits that are repeated over and over again. 0.2222222222… 2.43535353535… 0.142142142142… 6.801980198019… are all examples of recurring decimals 0.2222222222… 2.43535353535… 0.142142142142… 6.801980198019… are all examples of recurring decimals Dots are used to show how the decimals recur.

4 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 1000. If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

5 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 1000. If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

6 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 1000. If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

7 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 1000. If 1 digit recurs multiply by 10. If 2 digits recur multiply by 100. If 3 digits recur multiply by 1000.

8 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

9 Rational numbers include: all integers all fractions all mixed numbers all terminating decimals all recurring decimals some square roots some cube roots

10 Irrational numbers include: some square roots some cube roots some trig ratios

11 1 Which of these numbers are irrational numbers? Answer: and

12 2 Write each of these numbers in the correct place on the Venn diagram. Rational numbers Integers

13 3 Is x rational or irrational for this triangle? 10 cm x cm 24 cm Using Pythagoras Answer: x is rational

14 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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