Limiting Sum Question (1 Viewer)

[>> Lisa <<]

I was wondering if anyone can help me. this is probably a very easy question but i can't seem to get the right answer.

the question is:
write each recurring decimal as a fraction using Geometric Series

a) 2.88888888.....(8 is only recurring)
the correct answer is 2 8/9

b) 0.23333333......(3 is only recurring)
the correct answer is 7/30

thanks

 

[Pace_T]

a) 2.88888888.....(8 is only recurring)
the correct answer is 2 8/9


2 + 8/10 + 8/100 + 8/1000 .....
2 + 8[ 1/10 + 1/100 + 1/1000 +...]
2 + 8 [ a/ (1- r)]
2 + 8[ 1/10/(9/10)]
2 + 8/9
26/9

 

[nick1048]

a) The series is 2 + 0.8 + 0.08 + 0.008......

S = 2 + (a/ 1 - r)

where a = 0.8, r = 0.1

2 + (0.8 / 1 - 0.1)
= 2 + (0.8/0.9)
= 2 + 8/9
= 2 8/9

follow the same working out for the other question

 

[Pace_T]

b) 0.23333333......(3 is only recurring)
the correct answer is 7/30


= 2/10 + 3/100 + 3/1000 + ...
= 1/5 + 3[ 1/100 + 1/1000 + ...]
= 1/5 + 3[ 1/100/(9/10)]
= 1/5 + 1/30
= 7/30

 

[nick1048]

lol two methods... and both right, how cool

 

[>> Lisa <<]

thanks for your help nick1048 and Pace_T. it is very much appreciated.

 

[Trev]

lol two methods... and both right, how cool

They are actually the same method, you know
It's just you did it with decimals and Pace did it with fractions...