Recurring decimals

Question 1

How do you convert a recurring decimal into a fraction?

Answer 1

1) write the recurring decimal as n
2) multiply by 10/100/1000
3) subtract to remove the recurring part
4) divide by 9, 99, or 999 to write as a fraction

Question 2

What do you multiply by if:

1) 1 digit recurs
2) 2 digits recur
3) 3 digits recur

Answer 2

1) 10
2) 100
3) 1000

Question 3

Prove that the recurring decimal 0.24 has the value 8/33

Answer 3

n = 0.24242424…

100n = 24.24242424…
n = 0.24242424

99n = 24

n = 24/99 = 8/33

Question 4

Show that 0.473 (4 doesn’t recur) can be written as 469/990

Answer 4

n = 0.47373737

(STILL ONLY X BY 100!)

100n = 47.37373737
n = 0.47373737

99n = 46.9

n = 46.9/99

n = 469/990