SP #6: Unit K Concept 10: Writing a repeating decimal as a rational number using geometric series

Steps and Explanations!!

1. Write out the repeating decimal with the same type of number according to its placeholder.

2. Find your first term or "a sub 1" by getting the first repeating number (in this case 127) and change it to a fraction according its placeholder.

3. Find your ratio by getting the 2nd term and divide it by 1st.

4. Once you find your first term and ratio, write the problem in summation notation, plug in formula, and add the sum. When you plug in formula, it should be an infinite geometric series.

5. When you add the sum, don't forget to add the "whole number" or the number in front of the decimal.

  The viewer should pay special attention to the repeating number in order to know how to set up the geometric series with its right placeholder. To get to the right placeholder add the zeroes before the repeating number. Make sure to know your formulas such as the geometric sequence and infinite geometric series. When adding the number in front of the decimal in the problem, make sure to show full work (common denominator etc.).