Why a hundred

If percentages are just fractions, why bother with them? Why not keep using fractions?

Here's why. A factory is testing two biscuits. Sugar makes up 9/34 of Variety 1 and 13/45 of Variety 2. Which is sweeter? You can't tell by looking; you'd have to calculate.

Now say the same thing differently: sugar is 26.47% of Variety 1 and 28.88% of Variety 2. Instantly clear. Percentages put every fraction onto the same denominator, so any two can be compared at a glance.

But why 100, rather than 10, 50, 1000 or 43? In principle any number would do. Two reasons favour 100.

First, our number system is base 10, so 10, 100 and 1000 sit comfortably with decimals: 31% = 31/100 = 0.31. Moving between fractions, decimals and percentages becomes almost automatic.

Second, 100 is a sweet spot: big enough to give detail, small enough to hold in your head. The same fraction 9/34 could be written 2.647 per decem (per 10) or 264.7 per mille (per 1000). Per 10 is too rough; per 1000 is more precision than most questions need.

The idea is very old. Long before decimal fractions existed, people calculated in tenths, twentieths and hundredths. 'Per hundred' appears as early as the 4th century BCE in Kautilya's Arthaśhāstra: 'An interest of a pana and a quarter per month per cent is just. Five panas per month per cent is commercial interest. Ten panas per month per cent prevails among forests. Twenty panas per month per cent prevails among sea traders.'

Around the same time the Romans charged taxes of 1/20 and 1/100 on trade and auctions; and 15th-century Italian manuscripts write 'xx p cento', 'x p cento', 'vii p cento': our 20%, 10% and 7%.

And percentages are everywhere now:

• the human body is about 60% water by weight;
• ice cream is 30–50% air by volume;
• 45% of the world watched part of the 2022 FIFA World Cup;
• over 80% of teenagers worldwide get less than an hour of physical activity a day;
• about 99.86% of the Solar System's mass is in the Sun;
• an estimated 52% of the world's farmland is degraded.