 Let's take a look at problem 4.10 So to become good at math memorizing all formulas and procedures is generally a waste of time to become good at math understand the underlying concepts and to do this create your own solutions to problems think about problems think about how the concepts fit together and create your own solutions to the problems Memorizing a formula in a procedure. Well that a formula procedure is what you produce when you create your solution But memorizing those is a waste of time it is more important to create those solutions because if you can create the solution to a problem You don't actually need to memorize how you did it. You can just do it And again to emphasize if you watch this video you might get a higher bath grade It is conceivable that you might get a higher grade in a math class But you will learn less and you will be worse at math So the question you have to ask yourself is this what are you here for are you here to get a grade? Or are you here to learn and if the grade is the only thing that matters? Feel free to watch the videos, but if you actually want to learn don't watch the videos Don't watch the videos because if you watch the videos if you follow Formulas and procedures you're going to learn less and you're going to do worse at mathematics Let's take a look at this So here's a problem that here's a question or here's a problem to find to write a repeating decimal as a fraction and if you watch this video you will learn less mathematics, but Let's go ahead and proceed anyway, so Remember that when I write something like this This is a repeating decimal and that tells me the three is repeated endlessly after the decimal point So it helps if I write it out like this x is 0.333 Etc with the dot dot dot saying I'm going to keep repeating the threes Now we do want to find 10x and to the extent that this is a hard problem So a little bit of guidance is useful and so some of the guidance is well, let's find 10x let's see what happens and the Significance of 10x versus 2x or 5x or anything else is that when we multiply a base 10 Decimal by 10 Everything shifts over one place so 10x is easy so 10x everything shifts over one place and the dot dot dot Remember that I have an endless supply of threes afterwards So one of those threes moves up into this thousands place So 10x is going to be 3.333 repeating Well, what happens if I go 10x minus x? Well, let's think about that. I have 10 of something I subtract one of the somethings so that leaves me with well 10x minus x and if I subtract this from this all of the portion after the decimal point lines up so all that part is gone and I have three left by itself and 10x minus x is going to be 9x and now I could solve for x x is three ninths and there's my solution and It's convenient, but not absolutely critical to reduce that fraction three ninths gets reduced down to one third