Question

What is this decimal 0.1111 as a percent?

Answer 1

`11.11/100 or 11.11%` as percent literally means "out of 100"

Explanation:

`x/100=0.1111`

`x=0.1111x100`

`x=11.11`

`11.11/1000=0.1111`

Answer 2

See a solution process below:

Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore `x/100` can be written as `x%`.

`0.1111 = 11.11/100 = 11.11%`

Answer 3

See the explanation

Explanation:

`color(blue)("Preamble:")`
If a decimal is terminating (stops example `0.125`) or repeats indefinitely then it may be represented by a fraction. A fraction is precise whilst `color(red)(ul("a rounded decimal is not precise."))`

The wording percent can be split into two parts and each part has its own meaning.

'per'`->` for each of.
'cent'`->` 100. Think of centuary

Connection number 1
So for example 6% is 6 for every 100. The 6 is part of the 100`->6/(6+94) = 6/100`

Connection number 2
The symbol of % is `ul("a bit LIKE ")` a unit of measurment but one that is worth `1/100`

So `6% ->6xx%->6xx1/100=6/100`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question for 2 different assumptions")`

`color(purple)("Assumption number 1: The given value is a terminating decimal.")`

`0.1=1/10`
`0.11=11/100`
`0.111=111/1000`
`0.1111=1111/10000`

We need to turn the bottom number (denominator) into 100 to end up with the percentage.

Multiply by 1 and you do not change the actual value. However, we can change the way it looks.

`color(green)(1111/10000color(red)(xx1) color(white)("d")->color(white)("d")1111/10000color(red)(xx100/100) )`

`color(white)("dddddddd.d")color(green)(->color(white)("d")(cancel(1111)^(11.11)/color(red)(cancel(100))xxcolor(red)(1cancel(00))/(100cancel(00)) )`

`color(green)(color(white)("dddddddd.d")->color(white)("d") 11.11/100`

`color(green)( color(white)("dddddddd.d")->color(white)("d")11.11xx1/100=11.11%`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(purple)("Assumption number 2: The given value is an infinatley repeating decimal.")`

For this part just accept that for `0.3333...` where 3 goes on for ever
we have `0.33bar3=1/3` Note that the bar over the last 3 signifies a perpetual repeat.

Also note that `0.333bar3-:3=0.111bar1`

So `0.11bar1=1/3-:3= 1/9`

`1/9->color(white)("ddddd")(1xx100/9)/(9xx100/9) = (11.11bar1)/100 ->11.11bar1%`

The difference between the two solution is that the decimal percentage in assumption 2 goes on for ever whilst that in assumption 1 terminates