Student Problem 7: Unit K Concept 10

• What is this about?

This picture shows a problem from Unit K Concept 10 which is about how to write a  repeating decimal as a rational number using geometric series. This concept is very easy so there will be no calculator. We will learn to break the long repeated decimal into smaller sums. Using that information, we will have a sub 1 and then figure out what the ratio is by taking any term then divides it by the one that precedes. This will be an infinite geometric series because the numbers go on forever. All of these problems converges so that we can use the formula for them. If it diverges, there will be no sum.

• What does the reader need to pay attention to?

The reader should to pay attention at the end of the problem because there is a number before the decimal that breaks the pattern. So to make it easy to solve, the reader can just ignore the first number and only focus on the pattern behind the decimal. After figuring out what the sum of that 0.666666..., the reader can add the number, that is not included from the beginning, to the sum. That will be the final sum of S sub infinite. This problem will not be solve by using a calculator because when we solve the sum, we will multiply the numerator by the reciprocal of the denominator.