# fraction equivalent

• Nov 15th 2009, 06:47 AM
fraction equivalent
ok so, to find a fraction equivalent, of say example $0.123 123 123$

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

hence you get

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

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

thanks
• Nov 15th 2009, 07:43 AM
e^(i*pi)
Quote:

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

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

hence you get

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

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

$\frac{9854}{9999}$

This does not simplify
• Nov 15th 2009, 07:53 AM
HallsofIvy
Quote:

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

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

hence you get

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

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!
• Nov 15th 2009, 07:57 AM