ʕ•ᴥ•ʔ Converting Repeating Decimals to Fractions Made Easy

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A repeating decimal keeps repeating itself endlessly. Yet, no worries, you don’t need to have unlimited paper to write it down. We can convert it into a fraction for a clearer presentation. Let’s learn how in this session.

Hi, thanks for coming to this question right here. Wow this is a very weird question. I rarely see this on any other tests or quizzes, but let's say once in a while the teacher does give you this type of question. We're trying to figure out the fraction of 0.38. But not just 0.38, but a .38 that's repeating decimals, okay. So there's a little bit of a trick of doing this question, so you just have to follow what I'm gonna do right now, okay. So, first of all you're gonna right down "X", okay. Oh, so let me do a quick change of my pen here So you're gonna do "X" is equal to 0.38, okay. And these are the decimals right? Sorry about that. And the next thing you have to do is, you have to try to put the repeated decimals on the left side of that decimal sign, okay. So basically this is what's gonna happen. You're gonna change it to 38.38 with repeated decimals just here. So, in order for you to go from here to here, you multiply by 100, right? if you do that over here, multiplying by 100 you should get the same thing on the other side and that we get the same thing to both side of the equation, so I gotta 100x here as well, okay. Now just leave it at that and we come to the side over here. I'm gonna try one more time writing down the .38. It's just copying down the question, right. But this time, we're gonna keep the repeated decimals on the right side of the decimals, okay. In this case, it's already in that kind of format. So remember, this one right here, you trying to put the repeated decimals on the left side of the decimal sign, this one right here you trying to place on the right side. It's just happened in this case, it's already at on the right side, okay. Once you get this equation right here and this equation right here, so the next thing you have to do is just take this and subtract this; but there's a way to do this one right here. I'm gonna show you. I will recommend you rewrite them again, 38.38 repeat it here and just put the "X" here and 0.38. You're just copying down both equations down, okay. Now you're going to subtraction; the top minus the bottom. So "100X" minus "X" this is just a one, right? So it's "99X" and 38.38 minus 0.38, the 38 are gonna cancel, it's just gonna be 38. So the answer you're gonna get which is the fraction you're looking for is just the 38/99, okay. And that is the final answer you're supposed to get. Punch it in a calculator, magically you're gonna get the decimal answer that looks just like that, okay. Thanks for watching.

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NOW I FINALLY UNDERSTAND WHY THE DENOMINATOR WAS 99 NOT 100!!!!

XaceLeem

You make Algebra so easy to understand, you have helped me get much better prepared for my final! I wish I had found your videos in the beginning of my semester!

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