Student Problem #7 : Unit K Concept 10

• What is this problem about?

This picture covers a problem from Unit K Concept 10. This concept deals with writing repeating decimals as a rational number using geometric series. In this type of problem what you are basically trying to do is break down the decimal to discover the rational number or the sum of the decimal. After breaking down the decimal into repeating units you then are able to figure out the first term of the series and then the common ratio of the series which allows us to then plug it into the equation that has the sigma with the infinity sign. Then, you plug in a sub 1 and r into the summation notation formula in order to simplify and figure out the rational number. 

• What does the viewer need to pay special attention to in order to understand the concept?

In order to understand the concept the viewer needs to pay special attention to how the decimal is broken down. What we do is basically take the repeating decimal and set it as its own. Then we out an addition sign which then allows us to break down the decimal by putting zeroes in front of the repeating decimal. The point of this is to make sure that you get the correct value for a sub 1. Also, when you have wrote out the series it is important that you write the broken down decimal correctly so that when we divide one term to the other, we and up with the correct common ratio (r).