Question

What is 0.24 as a fraction?

Answer 1

`0.24` is 24 hundredths or `24/100`

Or

`24/100 = (4 xx 6)/(4 xx 25) = (cancel(4) xx 6)/(cancel(4) xx 25) = 6/25`

Answer 2

`6/25`

Explanation:

A decimal is constructed like this:

`ubrace("Count of 1's") + ubrace(("some count")/10)+ubrace(("some count")/100)+("some count")/1000+ ..`
`color(white)("dddd")0color(white)("ddddddddddd") 2color(white)("dddddddddd")4`

So `0.24` is the same as `2/10+4/100`

Multiply by 1 and you do not change the value. However, 1 comes in many forms

`color(green)(2/10+4/100color(white)("ddd")->color(white)("ddd") [2/10color(red)(xx1)]color(white)("dd")+4/100 )`

`color(green)(color(white)("dddddddddd.d")->color(white)("ddd")[2/10color(red)(xx10/10)]+ 4/100)`

`color(green)(color(white)("dddddddddd.d")->color(white)("ddddd")[20/100]color(white)("dd")+ 4/100)`

`24/100 = (24-:4)/(100-:4) = 6/25`