Taking percentages

let's get started with some problems let's see first problem what is what is 15 percent of 40 the way I do percent problems is I just convert the percentage to a decimal and then I multiply it times the number that I'm trying to get the percentage of so 15 percent as a decimal is 0.15 you learned that from before the percent to decimal conversion a video hopefully and we just multiply this times 40 so let's say 40 times 51 5 5 times 0 is 0 5 times 4 is 20 bring down put a 0 there and then 1 times 0 is 0 1 times 4 is 4 and you get 6 0 0 then you count the decimal spots 1 2 no decimals up there so you go 1 2 you put the decimal there so 15 percent of 40 is equal to 0.15 times 40 which equals 6 point 0 0 well that's just the same thing as 6 let's do another problem hopefully that didn't confuse you too much and I'm going to try to confuse you this time just in case you weren't properly confuse the last time what is 0.2 percent of let me think of a number of 7 so a lot of people's inclinations would just say 0.2 percent that's the same thing as 0.2 and if that was your inclination you would be wrong because remember this isn't point two this is 0.2% so there's two ways of thinking about this you could say that this is 0.2 over 100 which is if you multiply the numerator and the denominator by 10 is the same thing as two over a thousand or you can just do the technique where you move the decimal space over two to the left in which case if you're starting with point two you need to move the decimal space two to the left you go BAM whoops bam bam and that's where the decimal goes so it's point zero zero two this is key point two percent is the same thing as point zero zero two this can always trip you up and I've made this careless mistake all the time so don't feel bad if you ever do it but just always play careful attention to decimal and a percentage at the same time so now that we figured out how to write this percentage as a decimal we just have to multiply it times the number that we want to take the percentage of so we say point zero zero two times seven well this is pretty straight forward 7 times 2 is 14 right and how many total numbers do we have well how many total digits do we have behind the decimal point let's see it's one two three so we need one two three digits behind the decimal point so 0.2 percent of seven is equal to point zero one four and you're probably thinking boy that's a really really small number and and it makes sense because 0.2% that's if you want to think about it that's smaller than even 1% so that's even smaller than one hundredth and actually if you think about it point two percent is one five hundredths so and if you do the math seven one five hundreds of seven will turn out to be this number and that's that's an important thing to do it's always good to do a reality check because when you're doing these decimal and these percent problems it's very easy to kind of lose a factor of ten here they are gained a factor of ten so always do a reality check to see if your answer makes sense so now I'm going to confuse you even further what if I were to ask you for is 20% of what number number so a lot of people's reflux we might just be oh let me take 20 percent it becomes 0.20 and multiply it times 4 and in that case again you may be wrong because think about I'm not saying what is 20% of 4 I'm saying the 20% of some number is 4 so now we're going to be doing a little bit of algebra I bet you didn't expect that in the percent module so let X equal the number the number or this number let X equal that number and this problem says that 20 percent 20 percent of X is equal to 4 I think now it's in a form that you might recognize so how do we write 20 percent of the decimal well that's just point 200 or 0.2 and we just multiply it by X to get 4 so 20 percent that's the same thing as 0.2 it's same thing as point 2 oh but that last trailing zero doesn't mean much 0.2 times X is equal to 4 and now we have a level 1 linear equation but you didn't expect to see that so what do we do we we can either well there's two ways to view it you can just divide both sides of this equation by the coefficient on X so if you divide point 2 here you divide by 0.2 here so you get X is equal to 4 divided by 0.2 so let's figure that what 4 divided by 0.2 is see I hope I have enough space 0.2 goes into 4 I'm going to put a decimal point here and the way we do these problems we move the decimal point here 1 over to the right so we just get a 2 and we can move the decimal point here 1 over to the right so this point 2 goes into for the same number of times that 2 goes into 40 and this is easy two goes into 40 how many times well 2 goes into 4 two times and then 2 goes in zero zero times you can done that in your head - and 240 is 20 times so 4 divided by 0.2 is 20 so the answer is 4 is 20 percent of 20 and does that make sense well there's a couple of ways to think about it 20% is roughly what it is exactly 1/5 and right 4 times 5 is 20 that makes sense if you and still not sure we can check the problem let's take 20 percent of 20 so 20 percent of 20 is equal to 0.2 times 20 and if you do the math that also will equal 4 so you made sure you got the right answer let's do another one like that I'm picking numbers randomly let's say 3 is 9 percent of what so if X once again let's let X equal the number the number that 3 is 9 percent of you don't have to write all that well in that case we know that 0.09 X right point oh 9s assume things 9 percent of X is equal to 3 or that X is equal to 3 divided by 0.09 well if we do the decimal division 0.09 goes into 3 let's put a decimal point here I don't know me 0 so I'm going to need so if I move this decimal over to the right twice then I'll move this decimal over to the right twice so 0.09 goes into 3 the same number of times that 9 goes into 300 so 9 goes into 30 3 times 3 times 9 is 27 I think I see a pattern here already 33 3 away 9 is 27 you're just going to keep getting 33333 the threes are just going to go on forever so it turns out that 3 is 9 percent of you could either write it as thirty three point three repeating or we all know that point three forever is the same thing as 1/3 so three is nine percent of 33 and 1/3 either one of those would be an acceptable answer a lot of times when you're doing percentages you're actually just trying to get a ballpark so the precision might not always be the most important thing but in this case we will be precise and obviously on tests and things you need to be precise as well hopefully I didn't go too fast and you have a good sense of percentage the important thing for these type of problems is pay attention to how the problem is written if it says find you know ten percent of a hundred that's easy you just convert ten percent to a decimal multiplied 100 but if I were to ask you 100 is ten percent of what you have to remember that that's a different problem in which case 100 is ten percent of and if you did the math it would be a thousand I think I spoke very quickly on this problem on this on this module so I hope you didn't get too confused but I will record more