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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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Square Roots and Irrational Numbers

Square Roots and Irrational Numbers

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