Rational Numbers

CHECK YOUR ANSWERS✓ ON YOUR OWN ANSWERS 1) -1.2 2) -7.375 3) -0.27 repeating (the line should be over the 27) 4) …

Rational Numbers/a>

everybody loves cookies and if I give you the option of having 3/4 of a cookie 0.7 of a cookie or 2/3 of a cookie which one would you rather have welcome to anywhere back I’m Jeff Jacobson and today we’re going to introduce rational numbers okay so let’s talk about the cookies 3/4 of a cookie 0.7 of a cookie or two-thirds of a cookie now I don’t know about you but I want the most cookie I can get so if I’m looking at this I want to choose which one is greater well the problem is we’ve got fractions and decimals so it’s a bit tough to compare so what we need to do is choose one we can either make them all fractions or all decimals most of the time it’s going to be easiest to make them all decimals because if you try to do all fractions then to compare you also have to have common denominators which we don’t so most of the time you’re going to want to just change them all to decimals that’s going to be the quickest and easiest well 3/4 as a decimal hopefully you have that memorized that’s just zero point seven two five zero point seven is already good and then two-thirds I don’t know if you have that memorized it’s a good thing to have memorize if you don’t hopefully you know one-third that’s zero point three repeating that line means that number repeats that digit repeats over and over and over yet an infinite amount of time so zero point three three three three three forever if that’s one-third well then two thirds is just zero point six repeating okay so zero point six six six six six if you don’t have those memorized try two they’re going to help you out a lot you’ll see them all the time but if not you can always convert this to a decimal by dividing two divided by three and you will get the same thing now that they’re all decimals hopefully it’s pretty easy to see which ones greater or the greatest and that is 0.75 these both have seven in the tens place but then we have to go the next and if I wanted to I could add a zero there so it’s really 7,500 compared to 70 hundredths and obviously that is greater and don’t get confused 0.6 repeating is like zero point six six six six six forever but we don’t care about all the six at the end or going to infinity we’re looking here right up right off the bat at the tenths place seven is greater than ten so we don’t even care what’s after we already know that that’s actually the least so you have the option take three fourths of a cookie okay let’s first talk about what are rational numbers when you see rational numbers think ratio right it’s in the word rational the first part is ratio ah so rational numbers are just numbers that can be written as the ratio of two integers so a ratio we could write like a fraction right a to B can be written as a over B as long as B is not zero because remember if B is zero then that’s undefined right so as long as a and B are integers okay then you’re good you’ve got rational numbers now we might be you might be getting a little bit confused talking integers so I can rational numbers and you think your whole numbers and you get them all mixed up well let’s just do a quick little a little chart or a little graph here to help you remember what’s what well at the very basic we have whole numbers that’s what you dealt with when you were a little kid right one two three four five six seven eight you know keep going no negative numbers here okay no decimals right just whole numbers one two three four I’m sorry I should have zero there keeps going forever then we talked about integers right well integers include all the whole numbers but then it also includes alright let me integers but then it also includes the negative whole numbers so then we’ve got negative 1 negative 2 negative 3 negative 4 and so on but it also has all those whole numbers still now we’re getting into rational numbers now rational numbers includes all the whole numbers it includes all integers but now we are also going to talk about I should know ok we’re also going to talk about fractions and decimals so now that’s what we’re talking about rational numbers so zero point five three fours zero point three repeating let’s see 0.78 negative two thirds right negative four point five those are all rational numbers okay so that’s important hopefully that helps kind of break it down for you the difference between whole numbers integers and rational numbers rational numbers include all of this stuff here okay so let’s look at some examples of rational numbers and really go over this definition okay here’s some examples we’re kind of testing is it a rational number so can we write it as a ratio of two integers where the denominator is not zero so two is that a rational number well yet we can write that as 2 over 1 2 & 1 are both integers we’re good negative 3 can be written as negative 3 over 1 those are both integers remember negative 3 is an integer negative 1/2 well I can write that as negative 1 over 2 I can also write it as 1 over negative 2 those are both integers so that’s good 0.25 is the same as 1/4 that’s good those are both integers 0.6 repeating if you remember from earlier that’s the same as 2/3 so again those are both integers so all of these are examples of rational numbers okay an obvious example of a number that’s not a rational would be pi right pi continues forever never repeats so you cannot write it as a ratio of two integers like a over B so pi is not rational that’s irrational and there’s other examples but here’s some ones of rational numbers and that’s how you check let’s do an example okay example one right as a decimal so each of these we’re going to convert to a decimal fractions and decimals can go you can go back and forth between the two now negative two and one-fourth well I know that’s two wholes so that’s going to be negative two identical points going to be there and then I got to think well what is one-fourth as a decimal one-fourth as a decimal is 0.25 hopefully you have that memorized so that’s simply negative two point two five now another way to do it if you wanted to you can convert it to an improper fraction which would be right 4 times 2 is 8 plus 1 is 9 negative 9 over 4 and then this just means division so I can do 9 divided by 4 well that goes twice subtract I did a that’s 1 add a decimal point at a 0 4 into 10 is 2 again that’s 8 subtract I get to bring another zero down 4 to 20 is 5 and remember it was negative so negative 2 point 5 we get the same exact thing ok um now let’s look at the next one 5 11 again like I just said this line in a fraction that means division ok that’s really important ok I would definitely write that down so this means 5 / 11 so to convert it to a decimal that’s all we have to do 5 divided by 11 11 into 5 volt zero times so I add a decimal here at a decimal here add a 0 11 into 50 goes four times that’s 44 subtract I get 6 I’m not done at it is another zero bring it down and I get 60 11 into 60 goes five times that’s fifty five subtract I get five add a zero bring it down 50 11 into 50 is four and you might start to notice a pattern right that’s 44 subtract I get six it would be 60 again so four five again and it’s going to keep going on forever so the way that I write this as a decimal sense the four and the five are repeating I’m going to write it as zero point four five with the line over the four and the five that means the four and the five are what’s repeating okay this is called a repeating decimal okay because the four the five repeat over and over and over again for T zero point four five four five four five four five right on and on and on this one it’s not repeating it stopped it ended so we call that you could think of the movie The Terminator it’s called a terminating decimal so make sure you know the difference between the two terminating decimals they stop they end they terminate repeating decimals repeat on and on and on forever okay here’s some to try on your own alright example to write negative 0.26 as a fraction in simplest form well to be able to do that you need to know your place values so negative 2.6 I’m going to obviously my fraction is going to be negative so I’m not going to worry about that yet I’ll just kind of put that there and kind of forget about it a little bit and just concentrate on this 0.26 well if you know your place values this is the tenths place that’s the hundreds place so if you read it out loud to yourself and you can say 26 hundredths that gives you a kind of a hint as to what the fraction is going to look like 26 hundredths okay so maybe write yourself a little hit when you’re converting it from decimals to fractions read read it aloud okay use those place guys and that will give you an idea of what it’s going to look like as a fraction now the second part make sure it’s in simplest form well this is definitely not in simplest form they’re both even numbers so I can divide that by two and divide that by two and I get negative 13 over 50 okay and that is now in simplest form so that’s how you convert from decimals to fractions remember just read it out loud remember your place values and simplify it at the end okay here’s some more to try on your own thank you for watching and as always if you liked this video please subscribe you

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