Question

If the recurring decimal 0.84181 be written as a fraction in its lowest terms,the difference between the denominator and numerator is?

Answer 1

Let the fraction 0.84181 be x

Then 10x          = 8.41811111.....
          100x       = 84.18111111.....
          1000x     = 841.81111......
           10000x  = 8418.11111.....
           100000x= 84181.11111....

Therefore:  100000x           84181.1111.....
                   -10000x       = -  8418.1111....
                  90000x        =    75763.000

Therefore 90000x = 75763/90000
                  90000
      
                     x =  75763/90000

That is the fraction

The difference then is 90000 - 75763 = 14237