You know that . Can you predict what the decimal expansions of are, without actually doing the long division? If so, how?
Step 1-determine the decimal expansions of :
Given that
Multiply the decimal expansion of by
Therefore,
Step2- determine the decimal expansions of :
Multiply the decimal expansion of by
Therefore,
Step3- determine the decimal expansions of :
Multiply the decimal expansion of by
Therefore,
Step4- determine the decimal expansions of :
Multiply the decimal expansion of by
Therefore,
Step5- determine the decimal expansions of :
Multiply the decimal expansion of by
Therefore,
Hence, decimal expansions of are , ,, and respectively