Question

0.3178(178bar) in form a/b

Answer 1

Let 0.3178178178....... = x
So, 1000x = 1000*0.3178178178 = 317.8178178

Now, subtracting x from 1000x gives,
     1000x-x = 317.817817817-0.3178178178
 or, 999x = 317.5
 or, x = 317.5/999
 or, x = 3175/9990
 or, x = 635/1998.

∴ 0.3178(178bar) = 635/1998, where, a=635 and b=1998.