Question

How do you convert 1/12 into a decimal and percent?

Answer 1

`8 1/3% " "->" "0.0833bar3`

Explanation:

Lets do it the other way round and determine the % first.

% is like a unit of measurement and is worth `1/100`

So `x%` is the same as `x xx1/100=x/100`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Concept behind method")`

Initial condition`->" "1/12` but we need `x/100` so the 12 needs to be changed into 100.

First divide it by 12 to make 1 then multiply by 100 to make 100.

`12xx1/12xx100 -> 12xx100/12`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("The actual calculation for percentage")`

To maintain proportionality what you do to the bottom you do to the top (for multiply of divide).

Multiply top and bottom by `100/12`

Initial condition`->" "1/12 -> (" "1xx100/12" ")/(12xx100/12) = (8.333...)/100`

`8.333...` is the same as `8 1/3`

So we have `8 1/3%` as an exact value
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Converting this to a decimal value")`

We have `8.3333... -:100 = 0.083333...`

The 3's repeat for ever and a way of writing this is: `0.083bar3`
where the bar over the last 3 means that it is repeated for ever.