SP#6: Unit K Concept 10: Converting Repeating Decimals into Rational Fractions

 

Step 1: Start with the repeating decimal 5.212121... and find the a sub 1 and a sub 2 terms by taking the repeating terms out as chunks, using zeroes as placeholders where necessary.
Step 2: Divide the a sub 2 value by the a sub 1 value to get the ratio.
Step 3: Plug the terms into the summation notation for infinite geometric sums.
Step 4: Plug the terms into our sum formula and simplify.

For this problem, you needed to pay attention to the formulas used. Make sure you use the right ones! If you don't, you will get the wrong answers.