1. RATIONAL AND IRRATIONAL NUMBERS

2. Recurring decimals

3. 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.

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

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

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

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

8. 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

9. Rational numbers include:
all fractions
all integers
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?
x cm
10 cm
24 cm
Using Pythagoras
Answer: x is rational

14. 4 Is x rational or irrational for this triangle?
12 cm
4 cm
x cm
Using Pythagoras
Answer: x is irrational