Fractional form of repeated decimals

[eileen]

Hi, I am struggling with this question.
Could someone please explain how to do it?
If anyone is using Essential Further Mathematics Third Edition, it is Exercise 91 Q2b (Page 271)

Find the fractional form of the repeated decimal 0.16 (with a dot on top of the 6)

[brightsky]

Let

Hence ...(1)

and ...(2)

(2) - (1):

[eileen]

thank you so much! i understand that now.
how about 0.09 with dots on the 0 and 9

[m@tty]

Taking the same approach as brightsky:

Let (1)

  (2)

(2)-(1)

[eileen]

Taking the same approach as brightsky:

Let (1)

  (2)

(2)-(1)

why do we not times this one by 10? :S

[TrueTears]

Hi, I am struggling with this question.
Could someone please explain how to do it?
If anyone is using Essential Further Mathematics Third Edition, it is Exercise 91 Q2b (Page 271)

Find the fractional form of the repeated decimal 0.16 (with a dot on top of the 6)

[TrueTears]

thank you so much! i understand that now.
how about 0.09 with dots on the 0 and 9

Same principle



Here your starting number for the series would be 0.09 and common ratio is 0.01.

[m@tty]

Taking the same approach as brightsky:

Let (1)

 (2)

(2)-(1)

why do we not times this one by 10? :S

You can. But it doesn't work out as neat.



  (1)

    (2)

(2)-(1)

[TrueTears]

Eventually you should get: