Percent

Where the word comes from

Per centum — Latin for “by the hundred”. The sign is a squashed-up $100$, with the $1$ flattened into the slash and the two zeros left either side.

$$30\% = \frac{30}{100} = 0.3$$

One number, three costumes.

Why a hundred

Fractions can use any denominator, which is exactly what makes two of them hard to compare at a glance. Is $\tfrac{17}{40}$ bigger than $\tfrac{5}{12}$?

Percent settles on $100$ for everybody. Once both quantities are out of the same number, comparing them is counting — $42.5\%$ against $41.7\%$ answers it immediately.

A percent is a denominator the whole world has already agreed on.

Above one hundred

$100\%$ is the whole thing, not a ceiling. $150\%$ is one and a half times it, and anything that more than doubles has grown by over $100\%$.

A decrease is different: losing $100\%$ of something leaves nothing, so for a quantity that cannot go below zero there is nothing further to lose.

Converting

From	To	Do
percent	decimal	divide by $100$ — the point moves two places left
decimal	percent	multiply by $100$ — two places right
percent	fraction	write over $100$, then simplify

Going to a decimal makes the number smaller and to a percent makes it bigger, so checking which way the number should move beats recalling the rule. See what is a percent.