Today on Math Hacks
I'm showing you how to take a nasty, repeating decimal
and turn it into a beautiful fraction in just a few simple steps
 
The best part about today's lesson is  you're not even going to need a calculator
it is honestly that simple.
So what are we waiting for, let's hop in!
The first thing you want to do is make sure you have a repeating number.
So you can tell you have a repeating number if you have a bar over some decimals, now this means
These two decimal places are going to repeat in this pattern forever.
So we'll have 5.634545454545 and so on.
You can also see it sometimes without the bar and just an ellipsis written afterwards, that also means
that the 4 and 5 will repeat forever.
So step number one, we're going to start by setting this value equal to x.
We're going to convert this equation into two separate equations.
The first one I want to rewrite the equation so that the decimal place falls directly to the left of the first set of repeating decimals.
So in this problem the first set of repeating decimals is this 45 right here.
So I need to ask myself "what can I multiply 5.634545... by to get 563.4545..."
Now the easiest way to look at that is to say, well I need to move it two decimal places over, so I'm going to multiply by 100.
Because we have this equation, I'm going to multiply both sides by 100.
So that's going to give me: 100x equals 563.4545... repeating.
That's equation number one.
Now equation number two, we need to alter this original equation so that this time the decimal falls directly to the right of the first set of repeating decimals.
So that's going to be an additional two places over.
So all I need to move the decimal is one, two, three, four places.
So I'll be multiplying both sides of the equation by 10,000 this time.
Now believe it or not, we're almost there the next step is to subtract the smaller equation from the larger equation.
So since this one is 100x and this is 10,000x, I'm going to subtract the left equation from the right equation.
I'm just going to make sure that I am lining up the decimal places here to make it easy to subtract.
So  10,000x minus 100x is equal to 9,900x.
And on the right here I'm just going to do some basic subtraction. The decimal here, these are going to cancel out.
And for our final step here to convert this into a fraction, we're just going to solve for x.
And we can do this by dividing both sides by that 9900x.
So we get x equals 55,782 over 9900
And that is actually the answer. That is the fraction equivalent to this original decimal here.
Of course you can check that with your calculator simply by dividing these two numbers  to ensure that you do get 5.634545... repeating.
And that's all there is to it.
If you'd like a step-by-step guide on today's lesson jump on over to the Math Hacks blog where I have that waiting for you.
And if you found today's lesson useful, please give me a big thumbs up
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Till next time, I'm Brett Berry and this is Math Hacks.
