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A Whole Number Notation Scheme For Sub-Decimal Amounts In Bitcoin

Regardless of what wallet software we use, the bitcoin notation standard, i.e., how the numerals appear in your balance, is the primary UX component of our relationship with bitcoin. The punctuation of money, periods and commas, and where they appear in sequence, provide us with critical information regarding our personal wealth and the cost of goods. The notation standard is the drawbridge we must cross every time we interact with money.

In this article I propose a new notation standard for bitcoin which uses commas on the right side of the decimal point, with comma separators at the expected intervals for whole numbers, i.e., every three numerals counting from right to left. While this is a distinct break from customary notation, it instantly conveys the conversion rate between bitcoin and sats, and this is its sole utility.

.03445674 BTC

would be


A Shift Toward Sats

A confluence of factors are leading to more and more vocal support for denominating bitcoin entirely in sats. As sub-decimal amounts of bitcoin become more and more prevalent in the broader economy, awareness of the satoshi unit is growing. On Lightning, for example, where whole BTC amounts aren't yet used in production, denominating in sats is a must.

Despite the trend towards sats, whole number bitcoin denominations are still a part of life. The notation format outlined above unites bitcoin and sats in one visual representation.

What Problem Does This Solve?

If you interact with fractional bitcoin amounts long enough, the basics will become second nature. It took me probably two years before the idea that 0.5 bitcoin was equal to 50 million sats became intuitive. But there is a mental barrier to making this conversion quickly. The difficulty lies in the fact that while sats are universally counted in millions, the word “million” itself is a specific place measurement to the LEFT of the decimal.

0.5 BTC = 50,000,000 sats.

Fifty million is a whole integer amount, not a fractional amount. What we must come to grips with is that amounts expressed in sats imply a trailing decimal. The easiest way, then, to orient the user in notational space is to provide a comma separator every three numerals starting from the right, consistent with “million” in traditional notation.

It is only because Satoshi himself chose to add eight zeros to bitcoin and not nine, that we wrestle, subconsciously perhaps, with this conundrum of the third comma in satoshis. Had bitcoin been created with nine zeros, then the third comma would be in its proper place, whether you are reading from the right or from the left...


But since 1 bitcoin = 100,000,000 sats and not 1,000,000,000 sats, we are left with an awkward notational result, which is that in order to truly think in sats, we must insert a mental punctuation mark (a period) where it belongs: at the transition from 90 million to 100 million.

This issue does not exist in traditional finance because sub-cent values, which exist only in accounting, are always rounded up to the nearest tenth. In fiat terms, one-thousandth of a dollar does not exist. But bitcoin makes long strings of sub-decimal values necessary for the first time in economic history.

Because of the third comma conundrum and the new imperative to express eightdigit, sub-decimal strings, a new notational standard may be helpful. The scheme proposed above provides instant orientation and solves both problems.

Take a quick glance at the following numbers and narrate the sats conversion in your mind as you read. You will find it easy.





This notation standard is most helpful when making mental conversions between BTC and sats for amounts less than a million sats.

Say that you encounter the following amount:


In order to convert this to sats, the current notation standard leaves users with two options; either commit a conversion table to memory, or extend the zeros to the right when going from BTC to sats. The result is:


The problem with this exercise is that humans are not good at auditing amounts just by staring at a picture. After adding the zeros above, one must do at least one pass of error correction, double checking that the correct number of zeros have been added. It is a slow process.

Here’s another example:

698,000 sats.

In order to convert this to BTC we must do the same exercise above, but in reverse, extending the zeroes to the left and then adding a decimal. The result is:


While both of these conversions are mechanical and straightforward, they are cumbersome and must be done with painstaking accuracy. Being off by one zero is an expensive mistake.

The goal then is to create a notation standard which instantly accomplishes this conversion with a universally understood visual language, with built-in value signifiers to provide error correction at the first pass, and which allow the user to make value assessments without slowing down to count, then re-count, individual zeros.

Positive Feedback

The proposal has garnered a lot of discussion on Twitter.

The most surprising revelation was that I was not the first person to think of it.

Mark Nugent recently published this excellent essay. He and I have independently come to the same conclusions. His proposal is to use an apostrophe instead of a comma, which I also find appealing.

Another thing that surprised me was the overwhelming number of positive responses.

@BitSimple claims they are going to implement this in their app.

Carlo Campisi from Shakepay also tweeted that they are now looking into it.


Reaction to the concept was not 100 percent positive.

Matt Senter from the BTC rewards plugin Lolli said “😬No thanks. But I will update the email to use § notation.”

Among those who don’t like the idea, some common critiques emerged.

1 - Alternative grouping schemes

My argument against all of the above alternate format suggestions is that they don't mirror the traditional format of large numbers. Keep in mind this has nothing to do with fiat pricing. It's solely about accurate conversion between units. When I see 10,000,000 I know instantly that it means ten million. The commas, their placement, and the amounts they signify are all deeply embedded.

2 - Futureproofing

He's referring to the day when 1BTC=$1,000,000, and therefore one sat will equal $.01, or one penny. My response is threefold. The first is that any notation change wouldn't be implemented at the protocol level, but rather at the wallet level. It's a display parameter. If, at some future point, Bitcoin Core added digits to the right of the decimal, then wallet displays could easily be updated to reflect the 9th, 10th, 11th infinitum. The second part of my response is that a penny, in real purchasing power, is almost a non-existent denomination as things stand today. In a world where 1 BTC is worth $1 million, I don't know if goods will still be priced in pennies at all, so I'm not sure that adding a unit even smaller than that is necessary. Lastly, this won't actually become an issue until 1 BTC is worth $10 million. Per my above logic, we can easily revisit this question then.

Precisely. For sats only amounts, which will become more and more common in the economy (especially on Lightning) this notation becomes more and more useful.

3 - “Just use sats!”

This was far and away the most common critique.

I think that sats can and will be a prevalent standard. This eventuality, however, only amplifies the need to aid people in conversion to bitcoin. The more things are priced exclusively in sats, the more important it is that people internalize this ratio. But no matter how common sats are, whole number bitcoin amounts will continue to exist, and whole number bitcoin amounts will still be ubiquitous.

“Moreover, applications like exchanges and blockchain explorers will probably always use BTC as their bitcoin unit of choice because they need to list large and small amounts together in a common format. Consider this screen grab of a list of unconfirmed transactions...” — Mark Nugent


In closing, I'd like to turn briefly to the question of unit bias, and how this notation, in a roundabout way, helps to ameliorate the problem.

Postscript: The Decimal Does Not Equate To Smallness

Bias against numbers to the right of the decimal, the perception that they represent insignificant sums, is wholly appropriate to an inflationary system, where all values get continuously smaller in real terms. Bitcoin obviates this mode of thinking forever. For many of us, it will become daily practice to measure substantial wealth with a leading period. The satcomma standard (thanks for the name @ZoltanTokoli), essentially recreates whole numbers to the right of the decimal. Used in the context of money, this format retrains the mind to perceive the decimal place as a doorway to large sums.

This is a guest post by ProgrammableTx. Opinions expressed are entirely their own and do not necessarily reflect those of BTC Inc. or Bitcoin Magazine.