Recurring Decimals and decimals.

Question 1

Example….

Prove that 0.24 (both 2 and 4 recurring) = 8/33

Answer 1

Let n=. 0.242424242424242424242424…..

100n= 24.242424242424242424242424…..
- n= 0.242424242424242424242424…..

99n= 24
( divided by 99)
N= 24/99 = 8/33

Question 2

If one of the digits does not recur e.g. 0.473 (only 7 and 3 recur) what do you do?

Answer 2

Times the result fraction by 10 on the top and bottom.

Question 3

What can you also be asked to do?

Answer 3

Put it as a mixed fraction- normal steps and finally put top heavy fraction in simplest form and then mixed number.

Question 4

Fraction…. 1/100

Answer 4

0.01

Question 5

Fraction….. 1/10

Answer 5

0.1

Question 6

Fraction….. 1/5

Answer 6

0.2

Question 7

What do remember to multiply by……

Answer 7

10 if 1 digit recurs.
100 if 2 digits recur.
1000 if 3 digits recur.