Help with an easy question please (1 Viewer)

[Avoodibaba]

...I do 3 unit, and i'm stumped on this..

Express 0.157(all repeated) as a fraction.

I know its meant to be done with geometric sum or something, like

1/10 + 5/100 + 7/100 + 1/10 000 ....

but I just can't remember

Help would be much appreciated

 

[boxhunter91]

0.157157157157...
=157/1000 + 157/1000x10^3..
.:T2/T1 =1x10^=3
.:Limiting Sum = 0.157 / 1-(1x10^-3)
=157/999

 

[Avoodibaba]

ah ty

 

[tku336]

Much easier method:

Let x = 0.157157157 ...

1000x = 157.157157157...

999x = 157

x= 157/999

 

[Avoodibaba]

Last time i had one of these questions i used that method and got 0/2, they are testing y12/11 syllabuses and thus if you use that (which is essentially y9/10) i don't think they'll give you marks, or 1/2 at best.

 

[greenie1113]

are you serious?? ive always used that method...which one do you use??

 

[HSC_2009_]

Similarly How would you convert this to a fraction 0.23333...repeater

 

[biopia]

0.23333... = 1/5 + 3/100 + 3/1000 etc

Ignoring the 1/5, use the limiting sum formula for the rest of the sum, where a=3/100 and r=1/10
(3/100)/(1-1/10) = 1/30

Substituting this back into the initial sum, you get 1/5 + 1/30 = 7/30 = 0.233333...

=]

 

[tku336]

The easiest way again: Let y = 0.2 + 0.03333 ...Let x = 0.033333...100x = 3.3333390x= 3y = 1/5 + 3/90 = 1/5 + 1/30 = 7/30