That's a good question. Many prime numbers (83 is one) repeat after n-1 decimal digits (or a factor of n-1) where n is the prime number. So we could expect 83 to repeat after no more than 82 digits. In actual fact it repeats after half this number, 41, which is a factor of 82.
Here is the 41-digit recurring part without the decimal point:
01204819277108433734039759036144578313253
There is a complementary number formed by subtracting this from a row of 41 9's:
98795180722891566265060240963855421686746
Half the multiples of 1/83 use the first number for repeating digits, while the other half use the second number. Join the head and tail of the two different numbers. 58/83 uses the second number and starts at the 6 at the tail followed by the head: 0.698795180...674.