Why do we round cash to two decimal points (i.e. “your total today is $14.32”) instead of three decimal points ($14.325) or one ($14.3) or zero ($14)? Who came up with the idea of nickels and pennies? Why don’t we have half-pennies? Why do we have cents at all?
We used to have half-pennies.
I suspect the rest of it has to do with what was practical and useful at the time the system of coins was invented. Then we kind of end up stuck with the basic numbering system while inflation gradually makes the smaller coins useless and they get taken out of circulation. The five cent piece is the smallest coin in New Zealand these days, but prices are still given to the cent.
I’ve been in a few restaurants where the prices are just given in dollars.
I did a report yesterday and rounded the revenue figure down from $4,376,899,204.55 to $4,376,899,204.
There were half penny coins minted in the US. During the depression, many states created “tax tokens” worth 1/10th of a cent.
Why round to two decimals? Because that’s what we did for a long, long time with cash, and no one cares enough about 1/10 of a cent or less to bother changing the system.
I’d say you’re a dollar short!
To OP: Over the years, inflation has reduced the buying power of a penny to the level where these days, it’s feeling more and more like we should do away with it. Round everything to the nearest 5 cents. Unfortunately we can’t just jump to rounding to the nearest dime, because of the quarter.
But a couple hundred years ago pennies meant something substantial.
^ And maybe a day late?
A half penny in 1856 (last time they were minted) would be worth about 15 cents today because of inflation.
And yet for some reason we are still minting cents, nickels, and dimes.
@ OP: Way too much trouble, that’s why.
At 55 cents, shouldn’t you have rounded up?
For what it’s worth, the US actually has five monetary units, not two. There are ten mills in a cent, ten cents in a dime, ten dimes in a dollar, and ten dollars in an eagle. Nobody ever uses them as units, but they’re defined as such.
There’s no love (or remembrance) of the farthing?
Limmin and you are correct. I will have to notify Treasury on Monday.
Gas stations?
Originally, when we first became a country, we had Continental Dollars. Continental Dollar Notes (aka Continentals) had values from $1/6 up to $80. By the 1780s, Continentals had devalued to the point of being close to worthless.
This led to the coinage act of 1792. After the complete failure of Continentals, they decided to base the value the dollar on something a bit more stable, so they picked the Spanish Silver Dollar, which was widely used at the time.
They also created the following coins (according to Wikipedia):
Eagles $10.00
Half eagles $5.00
Quarter eagles $2.50
Dollars or Units $1.00
Half dollars $0.50
Quarter dollars $0.25
Disme $0.10
Half disme $0.05
Cents $0.01
Half cents $0.005
So if you want to know who is to blame for the creation of the modern nickels and pennies, it’s the U.S. Congress in 1792.
Half cents were last minted in 1857.
And in case you are wondering, “disme” comes from old French, and that comes from the Latin Decima, for 1/10th. “Disme” quickly morphed into “dime”.
Gasoline stations still use mills, just so that they can get that extra 9/10ths of a cent per gallon.
Gas stations price in a multiple of mills, but they’re still not really using them as units. Gas isn’t two thousand, nine hundred and ninety-nine mills a gallon; it’s two point nine nine nine dollars.
Hopefully your Treasury is more forgiving than my Treasury.
Last week one our transport providers (major international player) submitted an invoice for $163,580.00 plus GST (10.0%) of $16,358.01. (sic)
Where the $0.01 in violation of mathematics came from I don’t know.
Though it isn’t the first time they have done this. But when I submitted the validated invoice for payment without the erroneous 1c our Finance rejected it and demanded the invoice be validated including the 1c overpayment.
Whaddaya do? 
Don’t tell me, let me guess. You do thousands of these reports per day and the rounded off cents get whisked into an account where no one misses them.
The account is controlled by Mr D. Ask
Looks like pennies have been around since the 1300s at least, while dollars appeared in the 1500s. We don’t round money to two decimal places, it just looks that way. I’d say we (mostly) use integer cents or pennies, but have the custom of a period separator between digit 2 and 3. It’s a question of punctuating the larger aggregates of money, not subdividing the smallest.
Gas stations can do whatever they want. They’re part of the petroleum industry, which has all the money in the world.
Electronic payment now means that $ 25.04 is as meaningful and retrievable an amount as $25.00 with no more effort. While it originated to represent the cent as a commodity unit, the relationship of coins to items of value was subsequently eroded by inflation, and as others have noted has meant that in many countries the smaller small change has gone extinct. If we did not go to electronic payment but relied on coinage, then I suspect you’d have seen a transition to maybe single digit or rounded dollar amounts in time.