Question

How do you convert 4/25 into a decimal and percent?

Answer 1

Quite a bit of teaching about principles. The calculation should only take a few lines once you are used to these.

Percentage`->16%`
Decimal `" "->0.16`

Explanation:

`color(blue)("Teaching about percentage")`

Percentage is basically a fraction. However it is a special fraction in that the bottom number is fixed at 100.

Using an example of thirty percent.
There are two ways that a percentage can and may be written.

For our example we have `30% and 30/100`. These mean EXACTLY the same thing. If that is the case then we have:

`30/100 = 30xx1/100`

`30% = 30xx%`

If they mean exactly the same thing then `%` is another way of writing `1/100`

When using the shortcut what do they mean by: "multiply by 100 and put a `%` on the end" ?

Basically they are multiplying by 1 but in the form of `100/100`

`"something"xx1 color(white)("dddddddd")->color(white)("dddd")"something"xx100/100`

`"The multiply by 100 bit"color(white)("d")->color(white)("dddd")"something"xx100xx1/100`

`color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100xx%`

`color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100%`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the percent part of the question")`

`color(green)(4/25color(red)(xx1)color(white)("dddd")->color(white)("dddd")4/25color(red)(xx4/4))`

`color(green)(color(white)("dddddddddd")->color(white)("dddd") (4xx4)/(25xx4)`

`color(green)(color(white)("dddddddddd")->color(white)("ddddd")16/100)`

But this is the same as `16xx1/100` and `1/100` is the same as %. So we have:

`color(white)("dddddddddddddddd")color(green)(4/25=16%)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("The decimal part of the question")`

`color(brown)("The teaching bit")`

A decimal construct is such that we have:

units + tenths + hundredths + .....

Using an example: suppose we had the number 23.26

Units `->23 " "larr" Units is counting in 1's"`

Tenths `->2/10`

Hundredths`->6/100`

`23/1+2/10+6/100" "->" "23.26`
....................................................................................
`color(brown)("Back to our question")`

We have `16%->16/100`

So we have: `0/1+1/10+6/100" "->" "0.16`