# How do you write 2/11 as a decimal?

Nov 5, 2015

$0.18 \dot{1} \dot{8}$
The two dots above the last 1 and 8 indicate that they repeat indefinitely. You may also use a dash above them.

Oct 26, 2017

Suppose you do not have a calculator.

$0.18 \overline{18}$

#### Explanation:

For another IMPORTANT example have a look at
https://socratic.org/s/aKi5x5nx

It is important as it shows how to deal with zeros. In the above we have the answer $0.5909090909 \ldots$ which has a lot of zeros.
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$\textcolor{b l u e}{\text{Introduction to method}}$

We avoid the decimal point until write at the end

11 is more that 2 but we can and may write 2 as $20 \times \frac{1}{10}$ where the $\frac{1}{10}$ is an adjustment. The 20 is more that 11 so the division is a bit more strait forward.

We reintroduce the decimal at the very end by multiplying the answer by EXERY adjuster of $\frac{1}{10}$
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$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{w h i t e}{\text{dddddddd")20color(green)(xx1/10)larr color(brown)(" changed the 2}}$
$\textcolor{m a \ge n t a}{1} \times 11 \to \underline{11 \leftarrow \text{ Subtract}}$
color(white)("ddddddddd")9 larr" Remainder"

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$\textcolor{w h i t e}{\text{ddddddddd")90 larrcolor(green)(xx1/10) larrcolor(brown)(" changed the remainder}}$
$\textcolor{m a \ge n t a}{8} \times 11 \to \textcolor{w h i t e}{\text{d")ul(88 larr" Subtract}}$
color(white)("dddddddddd")2 larr" Remainder"

////////////////////////////////////////////////////////////////////////////
$\textcolor{w h i t e}{\text{ddddddddd")20color(green)(xx1/10)larrcolor(brown)(" changed the remainder}}$
$\textcolor{m a \ge n t a}{1} \times 11 \to \textcolor{w h i t e}{\text{d")ul(11 larr" Subtract}}$
$\textcolor{w h i t e}{\text{dddddddddd}} 9$

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$\textcolor{w h i t e}{\text{dddddddddd")90color(green)(xx1/10) larrcolor(brown)(" changed the remainder}}$
$\textcolor{m a \ge n t a}{8} \times 11 \to \textcolor{w h i t e}{\text{dd")ul(88 larr" Subtract}}$
color(white)("dddddddddd")2 larr" Remainder"

We are getting a pattern of repeats so we may stop at this point as we can see what that pattern is.

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$\textcolor{b l u e}{\text{Putting what we have got so far together}}$

$\textcolor{m a \ge n t a}{1818} \textcolor{g r e e n}{\times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}} \textcolor{w h i t e}{\text{d")=color(white)("d}} 0.181818$

As this is a repeating pattern we have $0.18181818181818 \ldots .$ going on for ever.

If we put a bar over a repeating par it mathematically indicates that they repeat for ever. So we can write:

$0.18 \overline{18}$