How do you convert ##3/8## to a percent?

37.5%

the word percent can be split into 2 parts

The part per means 'for each of' and the part cent refers to 100. Think of centaury or centimetre.

So this fraction is 3 per 8. We need some as yet unknown count per 100.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)("Shortcut method")##

##(3 -: 8) xx 100 " alternative notation " 3/8 xx 100##

giving ##37 1/2 %##

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##color(blue)("From first principles")##

We have ##3/8##

To keep proportionality of fractions you need to apply the rule: what you do to the bottom number (denominator) you also do to the top number (numerator)

We need to change the bottom number into 100

##(color(red)(3xx100/8))/(cancel(8)xx100/cancel(8)) = (37.5)/100##

##color(brown)("Look at the red top bit. It is exactly the same as the shortcut!")##

##color(blue)("So writing "37.5%" means " 37.5/100##