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Historically, non-decimal monetary systems were common. E.g. pound / shilling.

Every currency I can think of or have ever used is 'decimal' (where a higher/lower unit of currency is either a multiple or factor of 10).

Are all currencies used by countries nowadays 'decimal'?

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    By the definition you provided (all of the currency is either a multiple or factor of 10), is the US dollar even a decimal currency? We have quarters, which are neither a multiple or factor of 10. Or am I missing something? – bvoyelr Jan 7 '20 at 13:55
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    @bvoyler. Yes, you are missing that a quarter is 25 cents. The cent is a unit of currency, a quarter is just a denomination of coins. I.e the price of something wouldn’t be described as “2 quarters” but as “50 cents”. – Darren Jan 7 '20 at 14:54
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    @Darren AHHH! Now it's coming together. I shouldn't think this much so soon after Christmas vacation. – bvoyelr Jan 7 '20 at 18:21
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    @MooingDuck If a currency had 100 cents to the dollar and a 3 cent coin, it would still be decimal because the two units (cents and dollars) have a ratio that is a power of 10. – CJ Dennis Jan 7 '20 at 23:19
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    @MooingDuck If you like, the cent is a sub-unit of the dollar. A quarter is then a multiple of a cent, not a sub-unit of the dollar. :-) – CJ Dennis Jan 7 '20 at 23:35
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The word you're looking for is not "metric" but "decimal".

Pretty much all currencies are decimal these days except for currencies that have divisions where the sub-unit is no longer used as it's worth so little.

The only countries left with non-decimal currencies are Mauritania and Madagascar according to wikipedia

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    With OP's definition, Mauritania and Madagascar are metric/decimal, too, since 5 is a factor of 10. – Federico Poloni Jan 7 '20 at 17:49
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    @FedericoPoloni That does not make them decimal. Two hundred and twenty in a decimal system would be written 2 dollars 20 cents (which looks like 220) but in the Mauritanian system would be 44 dollars (which looks nothing like 220) – slebetman Jan 9 '20 at 2:04
  • @slebetman "Looks like 220" this is not how OP defined "decimal". It is a higher/lower unit of currency is either a multiple or factor of 10. – Federico Poloni Jan 9 '20 at 7:30
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    @FedericoPoloni It is how the OP defined decimal. You seem to understand it is the multipe is a factor of 10 but he said the multiple or factor is 10 – slebetman Jan 9 '20 at 7:40
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    OP's definition of "decimal" is unclear, doesn't seem to be consistent with what is normally called "decimal" (e.g. by @FedericoPoloni's interpretation (which I think is a reasonable literal interpretation), hours (or degrees), minutes and seconds would be decimal, but these wouldn't usually be called a decimal system), and probably is not what they actually meant. I think what most people would understand by a decimal system would be: "a monetary system is decimal if it has two or more units, where the value each unit is an integer power of 10 times the value of each other unit." – John B. Lambe Jan 9 '20 at 12:59
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The Wikipedia article Non-decimal currency explains the situation in full:

Today, only two countries have non-decimal currencies: Mauritania, where 1 ouguiya = 5 khoums, and Madagascar, where 1 ariary = 5 iraimbilanja. However, these are only theoretically non-decimal, as in both cases the value of the main unit is so low that the sub-units are too small to be of any practical use and coins of the sub-units are no longer used.

The official currency of the Sovereign Military Order of Malta, which retains its claims of sovereignty under international law and has been granted permanent observer status at the United Nations, is the Maltese scudo, which is subdivided into 12 tarì, each of 20 grani with 6 piccioli to the grano.

All other contemporary currencies are either decimal or have no sub-units at all, either because they had been abolished or because they have lost all practical value and not used.

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    That Maltese one is weird... It's like an alternative version of the old British system of the Pound, which was subdivided into 20 shillings, each of 12 pennies, with 4 farthings to the penny. – Oscar Bravo Jan 8 '20 at 11:19
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    Note that base 12 divides very well by 1/2/3/4/6/12 and that makes 'scudo' easy to divide by that numbers (i.e. split 1 scudo over 6 people evenly). At 'grani' level it makes it easy to divide by 5 (20=5*2*2). I have no idea why 3rd level (piccoli) was added, maybe grani was too big at some time in history, but it's base 6, so makes 'grani' divisible by 1/2/3. btw:Note how hours/minutes/seconds system is itself base-60 (5*12 - see 12?),and days/hours is base-24 (2*12 - see 12?) - again because it makes it easy to divide. Base-10 systems make it pretty hard to divide 100$ over 3 people evenly.. – quetzalcoatl Jan 8 '20 at 18:39
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    Which explains why there are 36 numbers on a roulette wheel ;-) Now, if only I could find a casino which will accept my scudi ... – Mawg says reinstate Monica Jan 9 '20 at 6:56
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    Interesting that only 60 years ago, the GBP was divisible into 960 parts, and only 50 years ago was still divisible into 480 (halfpennies). How soon before even 100 divisions is deemed too many..? – Tim Jan 9 '20 at 10:04
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    @Tim there was some discussion on this in the UK not too long ago, in case you're interested bbc.co.uk/news/business-48133093 – Max Jan 9 '20 at 13:32
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What about Japan? AFAIK the yen is not subdivided into lesser units, nor is it a subdivision of a larger unit. Even if denominations are issued in multiples of 10**n yen, that is arbitrary and doesn't fundamentally make the yen a decimal currency.

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    If yen had higher groupings (with different names) that were not powers of ten you might have a point, but there's no such thing. – briantist Jan 9 '20 at 19:04
  • Yen: Subunits - 1⁄100: sen (錢), 1⁄1000: rin (厘). – CJ Dennis Jan 9 '20 at 21:53
  • @CJDennis 1 yen is the smallest unit. The largest circulation denomination is 10,000 yen (~US$91.30). – John Jan 10 '20 at 2:22
  • @John_ReinstateMonica The yen has subdivisions that aren't used, but they're still decimal. – CJ Dennis Jan 10 '20 at 9:06

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