# How do you convert 0.27 (27 repeating) to a fraction?

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59
Apr 9, 2016

$\frac{3}{11}$

#### Explanation:

You can do this with a bit of algebra, let $x = 0.27272727 \ldots$

Now times by $100$ to get $100 x = 27.27272727 \ldots$

But we can get rid of that tail part now by taking off $x = 0.272727 \ldots$, so

$100 x - x = 99 x = 27$

Now just divide by $99$ to get that $x = \frac{27}{99} = \frac{3}{11}$

Then teach the underlying concepts
Don't copy without citing sources
preview
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#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

17
May 19, 2017

$x = \frac{3}{11}$

#### Explanation:

let $x = 0.272727272727 \ldots . .$

multiply $x$ by $100 \text{ }$ because there are $2$ recurring digits

$100 x = 27.2727272727 \ldots . \left[1\right]$
$x \text{ } = 0.2727272727 \ldots . \left[2\right]$

$\left[1\right] - \left[2\right]$

$99 x = 27$

$x = \frac{27}{99} = \frac{3}{11}$

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