# writing decimal numbers as ordinal?

How to write 0.1 (ordinal) percentile? E.g. for 1 it would be "first percentile". Would it be "0.1st percentile"?

• You're struggling because your premise is flawed: `0.1` isn't an ordinal number. Ordinal numbers are the positive (or sometimes nonnegative) integers, which suffice to order things. You can't say "Bob is 1st, Jane is 2nd, and Jill is 1½th", you would instead reorder and relabel: "Bob is 1st, Jill is 2nd, Jane is 3rd". For you example, you would say "Horatio is in the top tenth of the first percentile". Jul 21, 2016 at 10:20
• percentile is defined here as Each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable. So, by definition, percentile can only be a whole number from 1 to 100. Jul 21, 2016 at 10:44
• @fdb Yes, but we don't say `x` to the one-tenth, we say the tenth root of `x`. Ordinal numbers are integral. Jul 21, 2016 at 10:46
• You are misunderstanding what a percentile is. A score of 0.1% is within the first percentile. There's no smaller unit, otherwise you're using a different measure. Jul 21, 2016 at 10:46
• Don't write it as an ordinal. Let people pronounce it however they wish. Jul 21, 2016 at 12:05

I understand mathematically speaking this is impossible, but as to reporting on measures, my supervisor uses "below the 1st percentile" in written explanations. Prior to narratives we supply precise numbers in a table.

There's usually not a practical need to go below the 1st percentile or above the 99th percentile. This is because in most statistical examples, the standard deviations below the 1st and 99th percentile are too high to consider/analyse - at least in normal distributions. In very high samples of data (⪆100,000 items) and in cases like server-load monitoring or national census analysis - it is practical to measure in more precise increments.

"Ordinal" specifically denotes a scale "where the order matters but not the difference between values." I cannot find a definition which says that ordinal percentile increments have to be integers. It is important to note though, that using 0.1 increments requires data-size to be `10x` larger (1%'ile = [0.1, 0.2, 0.3...]). Moreover, you have to actually calculate `1000` 'ranks' in whatever analysis your doing. The fallacy in most cases goes something like this. The 50th% has a value of 10, the 51th% has a value of 20 --> since my value is 15, I must be in the 50.5th%. Anyone can understand the logical reasoning, but if you don't know the data within the ranks, you cannot approximate a more precise %'ile. !approximate-percentile!

This is why integers are usually the best option for most cases.

After a quick look on a few PubMed big-data analyses, people will just use exact values equivalent to something like 0.5%'ile or 97.3%'ile. But! They have calculated the correct increments, not aggregated - based on imprecise data. You can also use terminology like `<1th` or `44th < xth < 50th`.

Another important thing to mention: in 'ordinal' percentiles, you acknowledge each rank as greater than everything below it not including. So, even if I scored top of my class (of say 10,000) in a test, my percentile calculation would be: `9,999/1 = 99.xx%'ile` (xx depending on your floor function). It will never be 100, because I didn't do better than my own score! I guess if you want to be super mathematically pedantic, the correct way to say `<1th%` would be `0< xth% < 1th%`.

TLDR; To describe 'ordinally' the percentile ranks of <1% increments, you must have ample sample-size and individually calculate each rank - do not approximate. You can write percentiles how ever you wish, as long as you conform to the units used in calculations/results. It is usually not necessary to use such a small increment for rank, as in most cases it is potentially confusing, misrepresentative and excessive.

# TL;DR

I suggest reading it as a mixed fraction. Here's the formula:

`(Mixed-number ordinal) = (integral-part ordinal) + ("-and-") + (Hyphenated, fractional part)`

# Examples

```Numeric Percentile | In Words (Fractional denominators are powers of ten.) +--------------------+-------------------------------------------------------+ | 0.1 | zeroth-and-one-tenth percentile | +--------------------+-------------------------------------------------------+ | 23 | twenty-third percentile | +--------------------+-------------------------------------------------------+ | 23.05 | twenty-third-and-five-hundredths percentile | +--------------------+-------------------------------------------------------+ | 10.001 | tenth-and-one-thousandth percentile | +--------------------+-------------------------------------------------------+ ```

# Explanation

Consider the number `1.5`.

As opposed to reading the decimal number digit-by-digit (i.e. `one-point-five`), one can also read it as a mixed fraction (i.e. `one-and-a-half` or `one-and-five-tenths`).

When we use the conjunction `and` to join the integral and fractional parts, we have essentially created a compound noun; one where the integral part is the main noun, and the fractional part describes the integral part. Hence, only the integral part needs to change to ordinal form.

I suppose one could also say `zeroth percentile and a half`, but that stylistically feels awkward to me.

• Well, I guess in English syntax that makes some sense. In the relevant context (maths, stats, data-science), a zeroth percentile is undefined and has no meaning. Also, A percentile rank like 10.001, requires 100,000 individual ranks to be calculated if you want to group anything meaningfully. And you would probably need tens of millions of relevant data items to make any decent comparison among ranks. This kind of naming convention is needless. Apr 23, 2022 at 12:38

"Zero point first" is definitely wrong. I think you should say "the zero-point-one-th percentile", just as you say "x to the n-plus-one-th". Your spelling checker will mark this as wrong, but it is the only reasonable possibility.

• The outcomes that result from this approach sound ugly and unnatural. Should there be a "one-point-threeth" percentile, too? A "seven-point-twoth" percentile? Aug 17, 2017 at 10:47