Question
You know that 
Can you predict what the decimal expansions of
are, without actually doing the long division? If so, how?
[Hint: Study the remainders while finding the value of 
carefully.]
Solution
Yes! We can predict the decimal expansions of 
without actually doing the long division as follows:
To predict the decimal expansion of 
locate when the remainder becomes 2 and respective quotient (here it is 2). Then write the new quotient beginning from there using the repeating digits 1, 4, 2, 8, 5, 7.
Similarly,
