How to display numerical face values? [Risolto]

We now have a centralized system for face values, as described here. Following this, the question of how to display the numerical part has come up. It began with a discussion over whether 10⁄20 or 1⁄2 is best for a 10 shillings note such as this. The argument for 10⁄20 is that it reflects the underlying currency system of 20 shillings to the pound, the argument for 1⁄2 is that it is the correct numerical form (a reduced fraction) and ensures that all coins and notes worth half a pound show the same value.

It was also suggested that this method be applied to decimal currencies, so that a 1⁄2 franc would have “1⁄2” but a 50 centimes would have “50⁄100”. Another point raised asked whether values expressed as decimal should always come with a minimum of two decimal places. With the new centralized system, ensuring a consistent approach will be easier but it would be good to know what the wider community want to see in these fields.

My own view on fractions is that the reduced form should always be used.

Hello,

I would like to clarify how the software is currently implemented.

All face values are technically stored as fractions.

• If the denominator is a power of 10 (namely 10, 100, 100, etc.), the face value is displayed as a decimal number. The number of decimals reflects the value of the denominator. For example, a value of "1 jiao" is internally stored as 1/10 and displayed as “0.1”. A value of “10 fen” is internally stored as 10/100 and displayed as “0.10”.
   
• If the denominator is not a power of 10, the face value is displayed as a fraction. For example, if a value was entered as “1/12”, it is displayed as “1⁄12”. If the a was entered as “3/12”, it is displayed as “3⁄12”.

This way, a value of ½ franc can be displayed as “1⁄2” and a value of 50 centimes can be displayed as “0.50”. A display of “50⁄100” is currently not possible.

Note that this behaviour didn't change with the new way of storing face values in a centralized manner. The centralized storage will help in applying consistency for whatever display we decide to adopt.

It seems strange that denominations for a decimal currency system aren't consistently treated as decimal.

Here are the face values in numeric form for the 2023 coins from the United States: 0.01. 0.05, 0.1, ¼, ½, 1, …).

Why not 0.25 and 0.5? Any if fractions are used, why not 1/20, 1/10?

I believe that the situation in the U.S. is quite specific. Even if the currency system is decimal, the mindset doesn't seem decimal. People talk about quarters, not 25 cents.

ceh2019

My own view on fractions is that the reduced form should always be used.

Agree. This is also used occasionally on banknotes. ½ Mark [Polish notgeld], for example.

From Xavier's reply, it seems that decimal currencies are to be treated separately from non-decimal. This presumably means that the ¼ currently displayed on US quarters will, in time, be replaced by 0.25. I personaly have no problem with that, nor would I have a problem if a special case was made to keep ¼ for these coins.

Turning to non-decimal currencies, it seems that the plan is to have 10⁄20 for 10 shillings and 3⁄240 for 3 pence. Can I ask how coins such as 2½ shillings or 1½ pence are to be dealt with? We obviously can't have “2½/20” or “1½/240”, so what is the plan? Will these have to be special cases too?

Those two already have a value assigned, what is wrong with them?

Jarcek

Those two already have a value assigned, what is wrong with them?

Nothing except that they don't fit into the new model that's being proposed.

So I guess there is no need to change.

Jarcek

So I guess there is no need to change.

What about all the other coins that this proposal would change from reduced fractions? If the method of indicating the underlying currency system can't be applied to all, should it be applied to some or none?

Do you have an example please?

Jarcek

Do you have an example please?

Sorry, an example of what? This 10 shillings note shows a non-reduced fraction being used. My question is whether we should use these at all, given that we can't always use them, such as for the 2½ shillings and 1½ pence.

ceh2019

Jarcek

Do you have an example please?

Sorry, an example of what? This 10 shillings note shows a non-reduced fraction being used. My question is whether we should use these at all, given that we can't always use them, such as for the 2½ shillings and 1½ pence.

I personnally feel ok to have 10 shillings (10/20) and 21/2 shillings (5/40)

Compendium

I personnally feel ok to have 10 shillings (10/20) and 21/2 shillings (5/40)

So this takes things a stage further. Having 5⁄40 for a 2½ shillings piece is no longer reflecting the underlying currency system. How can we set out what the rules are? One could just as easily could argue in favour of 30⁄240, which does at least respect the currency system. This is why mathematicians use reduced fractions. They give a single form with no need for interpretation.

I would definitely say when a fraction is used make it an as small as possible denominator. The value is only in relation to the main currency unit, no need to make it about sub-denominations. If you don't know the denominations you can look them up on your own time in the headers of the currency.

Oh, now I see what seems to be the issue. I guess we should decide one way or another.

Jarcek

Oh, now I see what seems to be the issue. I guess we should decide one way or another.

As I see it, we have a choice between always giving the reduced fraction (my own preference) and a mix of forms including (where possible) fractions that reflect the underlying currency system. This mix would lead to the following for £sd if I've followed the argument correctly.

Farthing - 1⁄960

Halfpenny - 1⁄480

Penny - 1⁄240

Three-halfpenny - 3⁄480

Threepence - 3⁄240

Sixpence - 6⁄240

Shilling - 1⁄20

Florin - 2⁄20

Halfcrown - 5⁄40

Crown - 5⁄20

Half sovereign - 10⁄20

Would we be happy with this? I know I'm not. Nothing is inaccurate but, if the fraction is to be displayed, I'd prefer something more immediately understandable.

ceh2019

Jarcek

Oh, now I see what seems to be the issue. I guess we should decide one way or another.

As I see it, we have a choice between always giving the reduced fraction (my own preference) and a mix of forms including (where possible) fractions that reflect the underlying currency system. This mix would lead to the following for £sd if I've followed the argument correctly.

Farthing - 1⁄960

Halfpenny - 1⁄480

Penny - 1⁄240

Three-halfpenny - 3⁄480

Threepence - 3⁄240

Sixpence - 6⁄240

Shilling - 1⁄20

Florin - 2⁄20

Halfcrown - 5⁄40

Crown - 5⁄20

Half sovereign - 10⁄20

Would we be happy with this? I know I'm not. Nothing is inaccurate but, if the fraction is to be displayed, I'd prefer something more immediately understandable.

Only the halfcrown is not ideal… ; but I like the rest of it, why don't you ?
I truly like the fact we make sense of this fraction, based on the reference value; it allows the mind to see how denominations are intricated with each other

Compendium

Only the halfcrown is not ideal… ; but I like the rest of it, why don't you ?
I truly like the fact we make sense of this fraction, based on the reference value; it allows the mind to see how denominations are intricated with each other

The main reason is because they don't express the value in the most readily understandable way. Consider the following. You would have the florin as 2⁄20 and the halfcrown (if 5⁄40 is rejected) as 1⁄8. Which is larger? Anyone half decent at arithmetic will get the answer quickly but should that be required? If the florin is given as 1⁄10 (remember that the first florins actually have one tenth of a pound on them), the answer is immediately obvious, no arithmetic required. That's the reason mathematics always uses reduced fractions. To me, this is making sense of a fraction.

A more numismatic reason for preferring reduced fractions is that one can more easily see the progression of the denominations. This is information not necessarily apparent from the non-reduced forms, which really just repeat information already in the name of the denomination. Another reason, that might appeal to you as an admin, is that there is only one possible reduced fraction, making it easy to write and maintain the guideline. I can easily imagine arguments about whether this 2 Pfennige should be 2⁄240 or 1⁄120, especially given that this equivalent ½ Kreuzer will presumably have to remain 1⁄120.

A final reason is a case like this 1½ guineas note. It's value in Irish money was 1 Pound 14 Shillings 1½ Pence. There are two ways to express this, as a mixed fraction, 1 113⁄160, or as an improper fraction, 273⁄160. At the time the note went in, Xavier stated a preference for improper fractions, which is fine. If we take your acceptance of 3⁄480 for the three-halfpenny as a guide, this would become 819⁄480. Is that really better? If not, how do you write the guideline to exclude it? Perhaps, if you want to use this system, you could give us an idea of how you would write the guideline?

I agree such guidelines would go with several exceptions, which is never great.

I do not have such strong preference here, and will let Xavier answer directly as he's the one who suggested to harmonize in this direction, and who has most context about how values are currently displayed ^^

I see non-reduced fractions continue to be used in an entirely arbitrary way, such as here for Ireland.

Are we going to get some guidelines that generate consistency?

In general, it is conventional to display fractions in their simplest form.

5⁄20 10⁄20 please stop doing this, ¼ ½ are more appropriate, and the only way to ensure consistency.

Hello,

I understand I'm the only person thinking that “5 shillings = 5⁄20” and “10 shillings = 10⁄20” is more meaningful than “5 shillings = ¼” and “10 shillings = ½”, so I'll change to reduced fractions.

We should still discuss the case of decimal currencies. There are two questions:

• If we follow the concept of reduced fractions for decimal numbers, we should show “10 centimes = 0.1” (in the same way as we prefer ½ over 10⁄20). I believe it's much clearer and we reduce the risk of misunderstanding when writing “10 centimes = 0.10” and “1 decime = 0.1”.
  Should we accept this inconsistency and write  “10 centimes = 0.10” but “10 shillings = ½”?
   
• The United States and other countries have a decimal currency but a mix of decimal and non-decimal denominations. Should we write the quarter dollar as “¼” or “0.25”? Same for the demi franc: “½” or “0.50”?

I would prefer the value of US quarters be written as 0.25, to me it looks messy to have mixed decimals and fractions within a decimal currency.

It's standard to always write two digits after the point for a decimal currency. Therefore, fifty pence should be written as 0.50, even if the trailing zero is technically superfluous.

If we want to have decimal values for all decimal currencies, there are three simple options:

1. Always use the fewest possible digits.

2. Use the number of digits that corresponds to the primary subdivision.

3. Use the number of digits appropriate to the individual denomination.

Of these, only option 1 avoids inconsistency. Option 2 works fine for 50p (0.50) but not for ½p (has to be 0.005), whilst option 3 would give this coin the value 0.10 and this coin the value 0.1 due to the different ways the denomiation is represented on the coins. A more complicated compromise would be:

4. Use the number of digits that corresponds to the primary subdivision or the fewest possible digits, whichever is longest.

This would give 0.50 for 50p and 0.500 for 500 mils but also allow 0.0625 for this 6¼ centimes. All dimes and 10 cents would be 0.10 but you'd still “see” the underlying sytem in most cases.

My vote is for option 1 but I think option 4 is workable.

Hello,

Fractions are now shown in their reduced form (example: ¼ for 5 shillings).

Decimal denominations use the number of digits appropriate to the individual denomination (example: 0.1 for 1 décime; 0.10 for 10 centimes) or the fewest possible digits (example: 0.0625 for 6¼ centimes), whichever is longest.

This is a bit old but…

Xavier

Fractions are now shown in their reduced form (example: ¼ for 5 shillings).

Maybe it is done now... In the database can save all formats (text: 5 Shillings / non-reduced fraction: 5/20; reduced fraction: 1/4; numeric: 0.25) and display one or other fraction according to system preferences or, maybe, member settings.

Xavier

Decimal denominations use the number of digits appropriate to the individual denomination (example: 0.1 for 1 décime; 0.10 for 10 centimes) or the fewest possible digits (example: 0.0625 for 6¼ centimes), whichever is longest.

+1

About 0.10 or 0.1... in my case (and I suppose all euro users) if I think in 20 cent of euro, I expect see 0.20, not 0.2 (the euro has two decimals, not one).