+400 Find the first ten digits after the decimal point in the decimal expansion of \frac{7}{11}=0.abcdefghij\ldots without a calculator.
(Express your answer as a ten digit number.)
+410 Since 11 is a factor of 99, we suspect this is a repeating decimal.
We multiply top and bottom by 9, getting 6399.
Our suspicions are confirmed. In general, 0.¯abc…n is represented by ¯abc…n10n−1, where n is the number of terms.
So, 6399=0.¯63, so our answer is 6363636363.
