Thoughts on 1/7 and Other Rational Numbers: Index

I’m using the Twelve Days of Christmas (and perhaps a few extra days besides) to do something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series the decimal expansions of rational numbers.

Part 1: A way to remember the decimal expansion of \displaystyle \frac{1}{7}.

Part 2: Long division and knowing for certain that digits will start repeating.

Part 3: Converting a repeating decimal into a fraction, using algebra.

Part 4: Converting a repeating decimal into a fraction, using infinite series.

Part 5: Quickly converting fractions of the form \displaystyle \frac{M}{10^t}, \displaystyle \frac{M}{10^k-1}, and \displaystyle \frac{M}{10^t (10^k-1)} into decimals without using a calculator.

Part 6: Converting any rational number into one of the above three forms, and then converting into a decimal.

Part 7: Same as above, except using a binary (base-2) expansion instead of a decimal expansion.

Part 8: Why group theory relates to the length of the repeating block in a decimal expansion.

Part 9: A summary of the above ideas to find the full decimal expansion of \displaystyle \frac{8}{17}, which has a repeating block longer than the capacity of most calculators.

Part 10: More thoughts on \displaystyle \frac{8}{17}.






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