How do you write 2/11211 as a decimal?

2 Answers
Nov 5, 2015

0.18dot1dot80.18.1.8
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.

0.18bar(18)0.18¯¯¯¯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... which has a lot of zeros.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("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 20xx1/10 where the 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 1/10
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Answering the question")

color(white)("dddddddd")20color(green)(xx1/10)larr color(brown)(" changed the 2")
color(magenta)(1)xx11->ul(11 larr" Subtract")
color(white)("ddddddddd")9 larr" Remainder"

/////////////////////////////////////////////////////////////////////////
color(white)("ddddddddd")90 larrcolor(green)(xx1/10) larrcolor(brown)(" changed the remainder")
color(magenta)(8)xx11->color(white)("d")ul(88 larr" Subtract")
color(white)("dddddddddd")2 larr" Remainder"

////////////////////////////////////////////////////////////////////////////
color(white)("ddddddddd")20color(green)(xx1/10)larrcolor(brown)(" changed the remainder")
color(magenta)(1)xx11-> color(white)("d")ul(11 larr" Subtract")
color(white)("dddddddddd")9

/////////////////////////////////////////////////////////////////////////
color(white)("dddddddddd")90color(green)(xx1/10) larrcolor(brown)(" changed the remainder")
color(magenta)(8)xx11->color(white)("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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Putting what we have got so far together")

color(magenta)(1818)color(green)(xx1/10xx1/10xx1/10xx1/10)color(white)("d")=color(white)("d")0.181818

As this is a repeating pattern we have 0.18181818181818.... 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:

0.18bar(18)