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

2 Answers
Nov 5, 2015

#0.18dot1dot8#
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)#

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)#