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






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