16. Express .65853 (repeating) as a fraction

 

Let x = 0.65853658536585365853. . .

 

Multiply both sides by 100,000

 



 

Subtract the bottom equation from the top.

 

99999x = 65853

 



 

We should try to reduce this. Break the top and bottom up into products of primes.

 



 

So our fraction becomes

 



 

which reduces to

 



 

or

 



 

which you can check by dividing the bottom into the top.