In this video, ns wantto talk around how us can transform repeatingdecimals into fractions. Therefore let's offer ourselvesa repeating decimal. So let's speak I had actually therepeating decimal 0.7. And also sometimes it'llbe written prefer that, i beg your pardon just means thatthe 7 keeps top top repeating. For this reason this is the samething as 0.7777 and I can just store goingon and also on and on forever through those 7s. So the trick come convertingthese things into fractions is to basically setthis equal to a variable. And also we'll just showit, execute it step-by-step. Therefore let me collection thisequal come a variable. Let me contact this x. So x is equal to0.7, and also then the 7 repeats on and also on forever. Currently what would certainly 10x be? Well, let's think around this. 10x. 10x would simply be 10 times this. And also we can even thinkof it ideal over here. It would be, if wemultiplied this time 10, you'd be moving the decimal1 end to the right, it would be 7.777, on andon and on and on forever. Or you could say itis 7.7 repeating. Now this is the trick here. Therefore let me make theseequal to each other. Therefore we recognize what x is. X is this,just 0.777 repeating forever. 10x is this. And also this is anotherrepeating thing. Currently the means that we can getrid that the repeating decimal is if us subtract x indigenous 10x. Right? since x has all this 0.7777. If you subtractthat from 7.77777, climate you're simply goingto it is in left through 7. For this reason let's carry out that. So let me rewrite it below justso it's a little bit neater. 10x is same to 7.7repeating, which is equal to 7.777on and also on forever. And also we establishedearlier that x is same to 0.7 repeating,which is same to 0.777 on and also on and also on forever. Currently what wake up if yousubtract x from 10x? therefore we're going to subtractthe yellow native the green. Well, 10 that somethingminus 1 of something is just going to be9 of the something. And also then that'sgoing come be equal to, what's 7.7777repeating minus 0.77777 walking on and onforever repeating? fine it's just going to be 7. These components aregoing to cancel out. You're just left v 7. Or you could say thesetwo parts cancel out. You're simply left with 7. And also so you get 9x is same to 7. To settle for x, you justdivide both political parties by 9. Let's divide both sides by nine. I can do all 3 sides,although these space really speak the exact same thing. And you get x is equal to 7/9. Let's do an additional one. I'll leave this one hereso you have the right to refer to it. Therefore let's to speak I have actually thenumber 1.2 repeating. For this reason this is the exact same thingas 1.2222 on and on and on. Whatever the bar ison peak of, that's the component that repeatson and also on forever. So as with we did over here,let's set this equal to x. And also then let's speak 10x. Let's multiply this through 10. Therefore 10x is same to, itwould it is in 12.2 repeating, i beg your pardon is the same thing as12.222 on and on and also on and on. And then we cansubtract x indigenous 10x. And you don't haveto rewrite it, yet I'll rewrite it right here justso us don't get confused. For this reason we have actually x is equalto 1.2 repeating. And so if us subtract xfrom 10x, what carry out we get? on the left-hand side,we acquire 10x minus x is 9x. And also this is going to beequal to, well, the 2 repeating components cancel out. This cancels through that. If 2 repeatingminus 2 repeating, that's just a bunch that 0. Therefore it's 12 minus 1 is 11. And you have actually 9x is equal to 11.

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Divide both sides by 9. You acquire x is equal to 11/9.