# Does it make sense to display a decimal number such as 12.34 as Roman numerals? If not, how else?

I'm auto-converting any "Arabic" number in a text to Roman numerals.

This means that:

``````123
``````

Becomes:

``````CXXIII
``````

But what to do when I encounter decimals such as:

``````12.34
``````

? Should I really do:

``````XII.XXXIV
``````

? Decimals are a confusing concept in Roman numerals, certainly not made any easier because of the lack of information online.

My "algorithm" simply takes any consecutive series of digits (prior to being formatted) and considers that a separate number. So, in the text:

``````Sue had 5 ice-creams and she was 24 years old, with 1.5 hours to eat the ice-creams.
``````

... would be turned into:

``````Sue had V ice-creams and she was XXIV years old, with I.V hours to eat the ice-creams.
``````

Are there really no authoritative/definite/final "rule books" survived from the Roman empire to define exactly how these numerals/numbers/digits are supposed to be used and displayed?

In general, if you're going for authentic Roman numerals, you'd have to convert the decimal portion into one of the fractions that a Roman would use – or a sum of those fractions. Obviously, this is somewhat more straightforward for something like '1.5 hours' (for which there's also the single word sesquihora) than for '12.34' – though, for most people's purposes, 12.34 is close enough to 12-1/3 that they would probably just call it XII et tertiam (partem).

If the decimals are less straightforward, and/or if a very high degree of accuracy is required, Frontinus's work on aqueducts from the first century CE provides one example of how a sum of fractions can be used. In book 1, sections 38ff., Frontinus describes the diameter, circumference, and capacity of various pipes in terms especially of halves, thirds, sixths, twelfths, twenty-fourths, and two hundred eighty-eighths, using either the words for those fractions or a set of symbols for them.

For example, here's Frontinus's description of a fistula quinaria and a fistula senaria, using symbols:

fistula quinaria diametri digitum unum = –, perimetri digitos tres S = = – ℈ III, capit quinariam unam.

fistula senaria diametri digitum unum semis, perimetri digitos IIII S = £ ℈ II, capit quinariam I = = – ℈ VII.

• Twelfths: = is 2/12, = – is 3/12, and = = – is 5/12.
• Halves: S is 1/2.
• Twenty-fourths: £ is 1/24.
• Two hundred eighty-eighths: ℈ II is 2/288, ℈ III is 3/288, and ℈ VII is 7/288.

Therefore, a translation would be:

'Number-5' pipe: 1 digit plus 3⁄12 in diameter; 3 digits plus 1⁄2 plus 5⁄12 plus 3⁄288 in circumference; it has a capacity of 1 quinaria.

'Number-6' pipe: 1-1/2 digits in dimaeter; 4 digits plus 1⁄2 plus 2⁄12 plus 1⁄24 plus 2⁄288 in circumference; it has a capacity of 1 quinaria plus 5⁄12 plus 7⁄288.

This system works well for Frontinus and lets him achieve a remarkably high degree of accuracy. For example, for the circumference of a fistula quinaria, the total of the fractions given by Frontinus, when converted to a decimal value and rounded to eight decimal places, is 3.92713334. If pi is used, the diameter of a circle with a diameter of 1.25 units, rounded to eight decimal places, is 3.92699082. So he's within less than 2/10,000 of a unit.

Update

Here's an image of the quoted text, in case your device doesn't show the symbols correctly: And here's a version of the text that uses full words instead of symbols:

fistula quinaria diametri digitum unum, quadrantem; perimetri digitos tres, deuncem, scripula III; capit quinariam unam.

fistula senaria diametri diametri digitum unum, semissem; perimetri digitos quattuor, bessem, semunciam, scripulum; capit quinariam unam, quincuncem, sicilicum.

[Source]

• Now I'm curious as to why they went to 288ths instead of skipping over (or stopping at) 144ths. Feb 2, 2020 at 19:09
• Can you add a passage from Frontinus as an image as well, so that it would be readable across devices? Feb 2, 2020 at 19:41
• "close enough to 12-1/3" — did you mean 12+1/3 instead (or, equivalently, 12⅓)? Feb 2, 2020 at 21:06
• @Ruslan: That's a hyphen, not a minus sign; so equivalent to 12⅓ Feb 2, 2020 at 21:09