Roman numerals and currency

From Amit’s Thoughts

I find that Roman Numerals didn't "click" for me. At an intellectual level, I understand how they work. But they felt unintuitive. Until now!

Let's start with the simplified version:

I is 1. If you want more than 1 you write more of them: II is 2, III is 3, etc. But it doesn't keep going like this. IIII is 4 (yes, it is! I'll cover IV later). But 5 is too many, so they write it as V. Then we're back to adding I to count by 1: VI is 6, VII is 7, VIII is 8, VIIII is 9. But then at 10, they write X.

So the rule is to keep adding I but when there are too many you switch to another letter. XI is 11, XII is 12, XIII is 13, XIIII is 14, then XV is 15, XVI is 16, XVII is 17, XVIII is 18, XVIIII is 19, then XX is 20.

At XXXXX they switch to L. At LXXXXX they switch to C.

At CCCCC they switch to D. At DCCCCC they switch to M.

I get it. I understand the rules.

But it didn't click until I related it to something I use all the time: cash money. (note: at least I did, until the pandemic; I originally wrote this post in 2019 and just hadn't published until now)

I is like a $1 bill. II is like 2 $1 bills. III is like 3 $1 bills.

V is like a $5 bill. VII would be 7, which is a $5 bill and 2 $1 bills.

X is a $10 bill. L is a $50. C is a $100.

To represent $168, I'd use a $100 + $50 + $10 + $5 + $1 + $1 + $1. That's C + L + X + V + I + I + I. So it's the Roman numeral CLXVIII.

Sure, there are a few places it doesn't quite match up. Roman numerals don't have a $20 bill. And they sometimes (not always) use "subtractive" variants 4 = IV instead of IIII, 9 = IX instead of VIIII, and others. Romans were inconsistent about this, and Wikipedia has a list. But the idea of using monetary bills helped me build some intuition, turning it from purely intellectual knowledge to something I can better relate to.