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 .
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 , , and 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 , which has a repeating block longer than the capacity of most calculators.
Part 10: More thoughts on .