why can’t Roman numerals go beyond 3,999,999

432 viewsMathematicsOther

Or is it just non standard to go beyond that large of a number?

In: Mathematics

7 Answers

Anonymous 0 Comments

It can, and there are several ways.

The Roman numeral system is additive. M = 1000; MM = 2000. So if you write enough Ms, you can theoretically write a number as high as you want. Write 5000 Ms in a row, you’ll be up to 5 million.

But that’s impractical, and so it was also non-standard. You don’t usually write more than three, at most four of any single symbol in a row. To get to higher numbers, the Romans and later Medieval scribes [developed different ways](https://en.wikipedia.org/wiki/Roman_numerals#Large_numbers) of writing:

* CIↃ = 1000, and then the short form of CIↃ was ↀ. But then Romans would write a pair of arcs, C and Ↄ, around an I. This way of writing 1000 actually dates back to the Etruscans before them. Each extra pair of C and Ↄ would raise the value by another power of 10, so:
* CCIↃↃ = 10,000 (short form ↂ)
* CCCIↃↃↃ = 100,000 (short form ↈ)
* The Romans never actually wrote longer versions, but a theoretical CCCCCIↃↃↃↃↃ would be 10,000,000.
* The [*vinculum*](https://en.wikipedia.org/wiki/Roman_numerals#Vinculum), a line drawn over the figure.
* If the Romans drew a line over a figure, that meant it would be multiplied by a thousand. So X̅X̅X̅I̅I̅ would be equal to 32,000. Although “M” for 1000 did not actually develop until the middle ages, M̅M̅M̅M̅ would be an acceptable roman numeral way to write “4,000,000”.
* Additionally, any figure inside of a three-sided box was multiplied by 100,000. Using that notation, |X̅| would be another way to write a million, while |M̅| would be a single symbol that would indicate a hundred million.

Mixing and matching these conventions (which are authentic, centuries old, I’m not making them up at all) makes it relatively easy to write up to around 399,999,999, which would be |M̅M̅M̅C̅M̅X̅C̅| C̅M̅X̅C̅I̅X̅ CMXCIX, even without going the fully-non-standard route of just piling on Ms, and also without making up any new notations.

However, what’s true is that the limits of Roman numerals as they were actually used, starts to become apparent at this point; any higher, and you start having to rely on writing out four symbols in a row, or combining the system’s parts in ways that were never done historically.

The reason why the Roman numeral system was never extended any farther than this, is because neither the Romans nor medieval scribes ever needed to talk about larger numbers that we take for granted today: a billion, a trillion. If users of Roman numerals *had* ever needed to speak about much larger numbers, they might’ve started combining ↂ and ↈ with the *vinculum*. The current global population of 8,103,263,100 people might’ve been written something like this, for example: |ↇ̅ↂ̅ↂ̅ↂ̅M̅X̅X̅X̅| C̅C̅L̅X̅I̅I̅I̅ C

You are viewing 1 out of 7 answers, click here to view all answers.