Short Answer Type
Can you predict what the decimal expansions of 
are, without actually doing the long division? If so, how?
carefully.]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.
Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
Perform the division to check your answer.
where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Switch
