The Elegant Counting System continues from the previous post (Part Two).

On to fractions. This is where English gets pretty weird if you stop to think about it. Check out these fractions and what they are spoken as in English:

1/2 – One Half

1/3 – One Third

1/4 – One Fourth

5/7 – Five Sevenths

1/10 – One tenth

1/11 – One Eleventh

As in other parts of numbering in English, the pattern appears after three.

In ECS, they look like this:

1/2 – One Twoth

1/3 – One Threeth

1/4 – One Fourth (Same!)

5/7 – Five Sevths (A bit tricky but doable)

1/10 – One Ontieth

1/11 – One Onety Oneth

The weird thing here becomes switching “a twoth” for “a half”. It’s not really that bad though. Same number of syllables and totally regular pattern.

## Decimals

As for decimal numbers, here is how it would break down, following the conventions from the first post here (Part One). Remember that the negative numbers in the upper left of the 10 represent the number of zers (zeroes) to the right of the decimal point LESS one for the leading zer. For example, 10-1 is actually 0.1, 10-2 is 0.01, etc.

10^{-1} – One Onetieth

10^{-2} – One Hunth

10^{-3} – One Thouth

10^{-4} – One Onety Thouth

10^{-5} – One Hun Thouth

10^{-6} – One Milth

10^{-9} – One Bilth

etc.

The number 0.123 would then be read as one hun twoty three thouth (6 syllables) instead of One hundred twenty three thousandths (7 syllables). But the real savings comes from numbers like 0.777777 which would be sev hun sevty sev thou sev hun sevty sev milths (12 syllables) instead of the whopping seven hundred seventy seven thousand seven hundred seventy seven millionths (22 syllables!).

## Different bases

Another great application for a new counting system like ECS is in other bases. We all tend to use base 10 for most of our numbering needs. But some people (e.g. computer scientists) use other bases like base 2, base 16, etc.

Base 2 (aka binary) usually requires people to say the numbers individually. For counting in binary is looks like this:

0, 1, 10, 11, 100, 101, 110, 111, 1000

When people speak these in English they commonly say zero (zer), one, one-zer, one-one, one-zer-zer, etc. It gets confusing to call 10 as ten when ten is used in base 10. You may ask “Wouldn’t that also happen if everyone said onety?” Yes, but it would highlight what they were really saying. Base onety will default to being the same number of fingers the average human has. The binary sequence in ECS would be zer, one, onety, onety one, one hun, one hun onety, etc. The word ten just has too much association with base 10 IMHO.

## Elegant Counting System goes hexadecimal

What about base 16? BTW, you can give yourself a point if you read that as base onety six instead of sixteen. Let’s look at counting in that situation:

0-9 is same as before in base 10

10 is A in base 16

11 is B, 12 is C, 13 is D, 14 is E, and 15 is F.

Here is the cool part. The base 16 number 1A is usually read one-A. In ECS, it is read as onety A. 16 (10 in base 16) is onety.

With all of these new numbers, we need to revisit the ordinal numbers and get:

1Ath is the onety Ath item. Hey, it works!

Post comments below and also post when you use it in your daily life. I just used it in ping ping to call out the score (onety three to onety five is 13-15 for example).

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