What is a percentage?

Welcome to Maths Is Not Boring by kidopoly.com. I'm Mira! And I'm Finn! If you haven't already, tap follow wherever you're listening so you never miss an episode.

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Today, Finn, I want you to picture the very top corner of a phone screen.

Okay, I see the time, the little bars for the signal, and the battery icon.

Right! And sitting right next to that battery, there is a very strange little squiggle. A tiny diagonal line slicing perfectly between two little circles.

Oh, you mean the percent sign? It's completely everywhere. It's on my weather app, and I saw it printed on the side of a juice carton this morning, right next to the vitamin facts.

Exactly, but have you ever actually stopped and really looked at it? Why a line and two little circles? It doesn't look like a number, and it certainly doesn't look like a letter of the alphabet.

Now that you mention it, it looks like a completely alien symbol, or maybe a tiny face with a stick sliced right across it. It is actually pretty weird.

Today we are looking at a mathematical idea that is hiding in plain sight. It is a brilliant, invisible trick that lets you take absolutely anything in the entire universe, no matter how giant or microscopic it is, and compare it on exactly the same scale.

Okay, comparing anything on the exact same scale sounds like a superpower. But what does that little squiggly line actually mean?

It stands for a word you use all the time, percent. And the secret to what it means is hiding right there inside the word itself.

Per cent. Cent is like a century, right? A hundred years, or a centipede with a hundred legs.

You got it. It comes from old Latin words per centum, which literally means for each hundred or out of a hundred.

Out of a hundred. Okay, but who decided we needed to measure everything in the world out of a hundred?

For that, we have to travel back over 2,000 years, to ancient Rome, to the time of Emperor Augustus. Emperor Augustus?

So he was ruling this absolutely massive empire, stretching all across the world. Exactly.

Rome was booming, and there were giant public auctions where people bought and sold huge amounts of goods. Picture the noise, the crowds, the absolute chaos of a giant Roman auction.

And Augustus needed to collect a tax on all those sales to keep his massive empire running, to build roads and pay his armies.

Right, but the sales were all completely different sizes. How do you make a rule that works fairly for a tiny bag of grain and a massive herd of horses? In Augustus's Rome, for every hundred pieces of value sold, no matter what it was, the Empire would take exactly one. Just one piece out of every hundred?

Yes. The Romans had a specific name for it. They called it the centesima, which means the hundredth.

So the centesima was just taking one part out of a hundred. That actually sounds incredibly simple.

It is simple, but thinking out of a hundred is actually one of the most clever tricks in all of mathematics. Why is it a trick? Isn't it just counting? Because it lets you compare things that are completely different sizes without getting confused. Imagine you have a tiny little peppermint suite and I have an entire massive football stadium.

Okay, I'm holding a tiny suite and you're standing in a giant stadium with thousands of empty seats. Not a very fair trade.

Definitely not. If you try to compare them, your brain just sees tiny and huge. But if I ask you for 50% of your suite, what are you giving me?

Well, percent means out of a hundred. So if I imagine the suite made of a hundred tiny pieces, 50 out of a hundred, that's exactly half. I'd cut the suite straight down the middle.

Exactly! And if I give you 50% of my gigantic football stadium, you'd have to chop the whole stadium right down the middle, the grass pitch and all.

Wait, so 50% always means exactly half, no matter how ridiculously big or small the thing is.

Yes, that is the absolute magic of the idea. Half of a tiny suite and half of a giant stadium are both exactly 50%. They are suddenly on the exact same scale.

It's like you're taking the stadium and shrinking it down into a hundred boxes, and taking the suite and stretching it up into a hundred boxes, just so you can see them side by side.

That is a brilliant way to picture it, Finn. You imagine chopping whatever it is, absolutely anything in the world, into 100 equal boxes. Once you do that, everything makes sense.

Okay, I love the hundred boxes idea. But hold on, I'm stuck on something really important. What is it? If this was used in Augustus's Rome, did the Romans actually draw that little line and two circles sign on their auction scrolls?

Ah, that is the best part. No, they didn't. The sign we use today didn't exist in ancient Rome at all. Then where did the little squiggle come from? It is actually a ghost of human handwriting. Fast forwarding to the Middle Ages, merchants in Italy were busy buying and selling massive ships full of goods.

And they had to keep track of all their trades, their costs and their profits, writing everything down on paper with ink.

Exactly. In Italian, they called the idea percento, and they had to write those words down hundreds, maybe thousands of times every single day in their ledgers. Which is exactly what happened. Over time, their handwriting slowly changed. They started writing a P and a C, and they put a tiny little circle next to the C to stand for the letter O at the very end of the word cento.

So they just wrote PC circle to save time?

Yes, and as the years went on, they wrote it faster and faster. The letter P eventually vanished entirely. The C and the little circle squashed together and slowly changed.

Oh wow! So the C and the circle turned into the diagonal line and the two little circles hovering next to it.

Exactly. The modern percent sign is just the word cento, squashed by people writing too fast over hundreds of years.

unknown Haha!

That is wild! It's a ghost of messy handwriting. Just people trying to finish their maths faster. And now it's a famous symbol living everywhere.

It is beautiful, isn't it? An ancient mathematical idea used in Augustus's Rome, shaped by the rushing hands of Italian merchants, sitting right now on your glowing phone screen.

And because it just means out of a hundred boxes, that makes so much sense of my battery icon. If it says 100%, it means all 100 boxes of energy are completely full. It's the whole thing.

Exactly. 100% means the whole thing. The entire 100 boxes out of the 100 boxes. Nothing is missing.

But what if the weather forecast says there is a 50% chance of rain? How can the giant sky be divided out of a hundred?

It means if you had exactly 100 days with the exact same clouds, temperature, and wind conditions you see right now, it would rain on 50 of them. Half of the time, under these conditions, you would get wet.

The sky, a battery, a stadium, a suite?

It is. But because 100% means the entire whole thing. It tells us something very funny about the way people talk. What do you mean? Have you ever heard someone tell an athlete to go out there and give 110% effort?

Oh yeah, people say that all the time. Like, try harder than you ever have before.

But mathematically, it's impossible. 100% of your effort is all the effort you have. The whole thing. You cannot give 110% of yourself because you are only one whole person.

Haha, I'm going to tell my soccer coach that next time. Sorry, coach, the math says I max out at exactly 100 boxes.

Alright, Finn, it is time for the quiz.

Okay, I've got my 100 boxes lined up in my head. Let's do this.

First question. What does the word percent actually mean? Next one. Under which ancient Roman Emperor was this out of a hundred idea used for auction sales? Question three. What did the Romans call this one out of a hundred part? Here's number four. Half of anything, like a stadium or a suite, is always what percent?

Last question. The percent sign we use today started out as fast handwriting, in which language? Great job! Let's see how you did. The first answer is percent means out of a hundred, or for each hundred. For question two, it was Emperor Augustus. Number three, the answer is the Romans called it the centesima.

Question four, half of absolutely anything is always 50%. And the final answer is the sign came from fast handwriting in Italian.

I am never going to look at the top corner of my phone the same way again. It's not just a squiggle, it's an ancient Roman trick and a ghost of fast Italian handwriting all rolled into one.

I love that. A simple idea, surviving thousands of years just because it's so incredibly useful for seeing the world clearly. It's totally brilliant. If you love seeing ordinary things, like a battery icon, turn out to be extraordinary Roman history, please leave us a five-star review. Just scroll down and tap the stars.

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See you next time on Maths Is Not Boring. Bye!

What is a percentage?

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