How to Convert a Recurring Decimal Into a Fraction

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In order to convert a recurring decimal into a fraction, understand that 1/3 is equal to .333 repeating. Find out how to use a bar to denote a recurring decimal with help from a tutor in this free video on math lessons and study tips.

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Let's take a look at converting repeating decimals, recurring decimals into a fractions. So these are the basic ones that you want to memorize and actually once you memorize this, the whole process is pretty easy. So .333 repeating, that bar, means repeating, that's what we use it for Math. So .3333 repeating is 1/3. So, that's because, 33, .333 if you keep going is exactly 1/3 literally of 1. The other one that this relates to is .66 repeating which is exactly double this and so the fraction is exactly double this. So it's not 1/3, it's 2/3; 2/3 is double 1/3. The next one is 1/6. This one is not so common. This one you see a lot. This is by far the most important one on the board here. That's what you're going to see in your Math book, in your Math classes and even in real life. That's what you're going to see the most and this one too. This one doesn't come up so much but it's worth knowing; 1/6 is .1/6 and the six repeats so notice the bar. This is only over the six, that's the only thing that repeats in this one. Now yo actually don't need to memorize the double one on this because 1/6 doubled is actually 2/6, which is 1/3. So 2/6 reduces to 1/3 and that's why 2/6 is .33 repeating. Alright, the next one, the last we need to know is 1/9th; 1/9th is a good one to memorize 'cause it's easy. 1/9th is always .111 repeating. And anytime you take another version of that like 2/9ths, it's actually just .22 repeating. And notice I wrote three 1's and put the bar, I wrote two 2's and put the bar, it doesn't actually matter. In fact really all you need is that. A lot of those people do this just 'cause it gives you more of a sense of the number. So whatever you have here, 2/9th is going to be .22. Notice, 3/9ths is .33 repeating, which matches this and that's because 3/9ths reduces to 1/3.

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