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Rational Numbers

Added Mar 30, 2017 •

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hello everybody Welcome to our very first instructional math video hopefully you found it okay because we're going to go ahead and get started on our very first topic play first topic is rational numbers were going to talk in this video about what is a rational number and what can we do with them so let's get started a rational number is any number that can be written as a fraction any number that can be written as a fraction so some samples of rational numbers are two thirds  -1 111th is a rational number even a number like is a rational number because even though it doesn't look like a fraction it can be written as a fraction you can write it as 7 / 1 and therefore -17 is a rational number because it could be written like that and even a decimal like .25 is a rational number because we normally wouldn't decimal on the top of a fraction like that but could be written as 1/4 and so .25 is a rash all numbers most of the numbers that we use in life are rational numbers so we're basically talking about fractions and even decimals alright so here's your first practice problem make up an example of a rational number okay now that we got that out of the way let's talk about what can we do with rational numbers will we can convert fraction which is a type of rational number into a decimal so grab your calculator and let's get ready to roll alright if you want turn a fraction into a decimal it's really easy all you have to do is divide the numerator by the denominator so in this case we're going to do 3 you / for now just be careful it's not 4/3 it's 3/4 numerator / denominator or top / so if you have a calculator you can just punch in 3/4 or if you need to do it the long way you can put the three inside the division rocks in the floor outside and you can say three and four and four doesn't go into 3 but it does go into 37 * + 7 * 4 is 20 hey Dan I need a 30-28 and it's too and then you go okay for and a to know but you bring down the 04 in at 20.5 * 5 * 4 is 20 okay give me a no remainder and therefore 3/4 yes 0.75 stats are decimal version of before it's the same number just two different forms 3/4 and .75 and we did it by Justin Bieber top / Bob so all you have to do to turn a fraction into a decimal is top / bottom if you have a calculator it takes like 2 seconds to convert 1/5 into a decimal we're going to do what divided by what  yep that's right we're going to do 1/5 and then there you go our answer is 0.21 V is equal to 0.2 it's the same number just two different forms and they're both rational numbers 0.2 as a rational number because it's the decimal version of 1/5 all right now we're going to convert 17/20 to a decimal try it on y calculator  if you do it right you should get 0.85 cuz it's 17/20 alright what's 17 nights does it work on improper fractions where the numerator is like bigger than the denominator and stuff yeah actually perfectly fine if you do 17/9 you get a boy what if it's a repeating decimal that's fine you just write it with that little bar over cuz it's 1.88 forever and sometimes that happens as well is one point repeating 8 still a rational yeah because it can be written as 17 nights alright this is what we call a repeating decimal  if there is no repeating pattern and a split ends at 0.85 it's a terminating decimal you might want to write that down repeating decimals terminating decimals so now it's your turn to try another practice problem convert 7/8 into a decimal  and then once you've done that MC grout is it a terminating decimal or a repeating decimal just for practice take 1415 sand turn that into a decimal to  and say whether that's terminating repeating okay so these are rational numbers and we're just making sure we know how to handle them  by the way when we did one fifth you turned it into a decimal and we did it on our calculator can we check to make sure that we did it right sure we can check to make sure that we did it right because what we got from one next was 0.2 or another way to say that is 2/10 right because two is in the tenths place remember our place values we'll talk about that and then doesn't 2/10 reduce to make 1/5 so good to turn 1/5 into .2 fixin to turn point to back into 1/5 works and therefore 1/5 equals itself and we feel pretty good about her answer king of this process we're going to now talk about how do you take a decimal and convert it back into a fraction so it's really the same thing we just did it's as backwards all right in order to do this we have to understand our places are place values so you probably know this is the tens place and this is the ones place that's the hunger play some this to right here is in the thousands place cuz it's 2345 what about the decimal ones on the right hand side have the. That 6 is in the tenths place that 6/10 the seven is in the hundreds place and the eight is in the thousands place and you can delete figure out where we go from there to 10,000 the millions and all that good stuff where did decimal into a fraction this nine is in the tenths spot so that 0.9 is really 9/10 we just turned a decimal into a fraction see how easy that was you just say it you write it the way you say it 9/10 but now it's a fraction okay so to turn a decimal into a fraction use tens or hundreds or thousands etc etc depending on the length of the decimal 0.8 is 8 in the tenths spot oh but you can reduce that so you probably should  alright what is a 0.73 will that 73 but it ends not in the 10 spot it ends in the hunt Spotswood 7300  alright and 0.44 is 4400 again you can reduce that so do it alright what if it's 899 that's 899 and it's not in the tents or the hundreds it's in the thousand $0.02 - $899,000 Yeezy so if you're going to turn 0.65 into a action we would say it's 13 wait a second  13/20 I thought it was supposed to be 65 / a hundred oh wait 65 over 100 reduced to 13/20 so its 6 but we should reduce it to 13 right now it's your turn what is 0.3 as a fraction  and then another practice problem what is 0 5 as a fraction alright once you master that you're pretty much good to go except one last saying about rational numbers what if it's a repeating decimal What If instead of just .8 it's a .8 repeating well it's not really the same as 8/10 because does it end in the tenths place no does it end in the hundredths place not really good never really actually ends so do we put 8/10 or do you put 8 over 100 or do we pay it and we can't really do any of that here's the trick on repeating can you just kind of have to know the trick to change a repeating decimal into a fraction instead of tents or hundreds or thousands we're going to use knights 99 or $999 or something like that so all we had to do is put 8 over 9 instead of 8 over 10 that was easy this would just be 3 / 9 instead of 3 / 10 and then you can reduce it to one third and maybe you even knew that one third is can you repeating what about .17 repeating it's going to be 17 but it's not going to be 17 over a hundred in the hundredths place it's going to be 17 99 in that's the really simple trick to do with repeating decimals so if you understand that then you can do this one last practice problem and then you'll be what's tonight's video notes convert 0.6 repeating into a fraction  what what was that did that oh my gosh you are done thanks for watching your very first instructional math video feel free to pause and go back and Rewind or anything you need to do to help you make sense of this and if you had any question throughout this video just write them down in your video notes and we will cover it tomorrow in class adios amigos

Uploaded by Jeff Marbut.

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Rational Numbers

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