1. ## fraction equivalent

ok so, to find a fraction equivalent, of say example $\displaystyle 0.123 123 123$

we put $\displaystyle s = 0.123 123 123$ therefore the repeating group is 123 and is 3 digits long so we multiply $\displaystyle s$by $\displaystyle 10^3$ ...
$\displaystyle 1000s = 123. 123 123 123 123 ... = 123 + s$

hence you get

$\displaystyle s = \frac {123}{999} = \frac{41}{333}$

So on that basis, how could you do the same for say, 0.985 498 549 854....

thanks

ok so, to find a fraction equivalent, of say example $\displaystyle 0.123 123 123$

we put $\displaystyle s = 0.123 123 123$ therefore the repeating group is 123 and is 3 digits long so we multiply $\displaystyle s$by $\displaystyle 10^3$ ...
$\displaystyle 1000s = 123. 123 123 123 123 ... = 123 + s$

hence you get

$\displaystyle s = \frac {123}{999} = \frac{41}{333}$

So on that basis, how could you do the same for say, 0.985 498 549 854....

thanks
Look at one repetition and put the same number of 9s on the bottom. Here it would be 0.9854 repeating to give

$\displaystyle \frac{9854}{9999}$

This does not simplify

ok so, to find a fraction equivalent, of say example $\displaystyle 0.123 123 123$

we put $\displaystyle s = 0.123 123 123$ therefore the repeating group is 123 and is 3 digits long so we multiply $\displaystyle s$by $\displaystyle 10^3$ ...
$\displaystyle 1000s = 123. 123 123 123 123 ... = 123 + s$

hence you get

$\displaystyle s = \frac {123}{999} = \frac{41}{333}$

So on that basis, how could you do the same for say, 0.985 498 549 854....

thanks
I'm glad e^(i pi) answered this one. I don't think I would have seen that this was 0.9854 9854 9854... ! I was wondering what repeated!

4. Thanks - i was looking at it as two lots of repetitions, ie 98 and 54 rather than 9854 together.