# Why are currency conversion quotes the wrong way round?

I notice that sites such as Google Finance quote the pound to dollar conversion rates in the form GBP/USD = 1.4784. I would read this as "GBP per USD = 1.4784" or equivalently "1.4784 GBP per USD" which is obviously the wrong way round.
When we quote speeds for example we say mph (or m/h) = 50 - meaning there are 50 miles for each hour. It's the same with all other rates in the physical sciences. And to calculate the rate of a/b (i.e. a per b) you just divide the number of a's by the equivalent number of b's.
So why do economists use an illogical and misleading convention?
Thanks Thomas

It's 1 GBP divided by 1 USD. The / is a normal division symbol.
Speed is an entirely different concept to currency conversion. To me, a/b doesn't mean a per b, it means a divided by b. The use of a slash as a shorthand for "per" is entirely different to its use in mathematics. And currency conversion is a simple mathematical calculation.
It's perfectly logical and not misleading at all. The misleading use of a slash is to use it to mean something other than "divided by".
Mark

On Tue, 14 Apr 2015 18:45:58 +0100, Thomas put finger to keyboard and
That can't be right - 1 divided by 1 is 1 !
Logically, it has to be 1 GBP divided by the equivalent number of USD or alternatively the cost of some appropriate asset (e.g. gold) in GBP divided by its cost in USD. Either way, you won't get GBP/USD = 1.4(ish)
How is speed entirely different from currency conversion - they both allow you to convert from one unit to another (or alternatively to convert the rate of change of one unit with respect to another). The 'per' and 'divided by' interpretations are equivalent. To calculate the number of miles per hour we're travelling we divide the number of miles by the time taken to travel those miles.
I beg to differ :-)
Thomas

Which, if you look carefully, is why it's 1 GBP divided by 1 USD. The units matter.
You can't "convert" distance into time. You can't go to a hypothetical physics bank and say "here are some miles, please can I have the equivalent number of hours". Speed is a measurement in its own right, not the result of a calculation of two different units of the same thing. Distance and time are not equivalents. They do not do the same thing.
Currency conversion, on the other hand, is simply the calculation of relative values of different units of the same thing: money. GBP and USD are both units of money, they both do exactly the same thing. You can, therefore, convert between them.
Mark
I appreciate your efforts, but nothing you say makes much sense to me.
Clearly there is a long established convention of GBP/USD not meaning GBP per USD (nor GPB divided by the equivalent value in USD) and we have to live with that. But to someone brought up in the physical sciences it's neither logical nor informative.
Thanks Thomas
Talking to myself again :-)
Look at it another way.
If I want to convert \$100 to £'s then I need to multiply by something that has units of £/\$ - aka GBP/USD. But clearly the conventionally quoted GBP/USD rate won't do that, instead I need to divide my dollars by that rate giving me something which has units of \$^2/£. It's crazy, no wonder economics doesn't qualify as a science :-)
Thanks Thomas
Hm!
Try 1GBP = 1.4784USD.
Moving the USD on the right of that equation to the left of the = sign puts it under the GBP.
Also 1GBP / 1.4784USD = 1. The different units cancel out to give a number because they are related. They are both units of money which have a defined relationship between them.
at 20:29:38:
Parse it as (value_of(GBP,1) / value_of(USD,1)) and it comes out right.
Remember it that way, as relative _value_, and they'll all come out right. Cf

So GBP/USD = 1.4784. How do read that, surely not as pounds per dollar = 1.4784.
But continuing with the theme of preserving units. To convert \$100 to £'s we need to multiply by £/\$ which in your case is 1.4784 - so \$100 = £147.84 :-)
Thomas

Yes, indeed. That's a very good way of notating it. But I suspect that it may be too difficult for a non mathematician (or non-programmer) to grasp.
Mark

The value of a pound divided by the value of a dollar (which seems to me to pounds per dollar before spread and commission).
GBP and USD are both units with dimensions of money.
You're overthinking it.
There's 1.4784 of the smaller ones to the bigger one. EVERYBODY knows dollars are smaller than pounds.

It's simple mathematics, obviously no longer taught in schools.
GBP/USD=1.4784
Therefore, multiplying each side by USD:
GBP=1.4784 x USD
Or, to verbalise it:
1 GB Pound equals 1.4784 US Dollars.
Or do you need pictures as well?

On Tue, 14 Apr 2015 22:34:36 +0100, Iain Archer put finger to keyboard and
That's quite a mouthful. Imagine if we expressed the cost of lemons as the value of £1 divided by the value of 1 lemon! I think most people would prefer the inverse - £'s per lemon or £/lemon (£/kg, £/m, £/hour etc. etc..). Given that there is a well established way of reading the slash - why introduce a contrary one?
Still looks a about t to me. Why not just express the value as a simple conversion rate - i.e. if you want to convert \$ to £ you multiply by the published £/\$ rate.
I suspect the reason economists like to use the inverse of the conversion rate is that a high value of that corresponds to a high value of the pound. Big number good, small number bad - sounds about the right level of sophistication for forex traders :-)
Oh well, no big deal I suppose.
Thanks Thomas
Like I said. Overthinking.

Yes, but that's because lemons and pounds are different types of thing. One is a physical object, the other is a unit of currency.
On the other hand, GBP and USD are the same type of thing. They are both units of currency.
The well-established way of reading the slash in a mathematical context is "divided by".
Mark

Irrelevant. If a shopkeeper were selling dollars I'd expect to see them priced at £0.67/dollar just as I'd expect to see his potatoes priced at £2/kg.
And I already showed how the two are totally equivalent - e.g the speed of a journey in mph (or m/h or m h^-1) is just the length of the journey in miles divided by the duration of the journey in hours! And like speed, I'd prefer a quantity which allows you to easily convert from one unit to the other (miles to hours or pounds to dollars) in a way which is consistent with the units of the conversion rate.
Thanks Thomas
It is, of course, dollars per pound.

By which I assume you mean £1 is equivalent to \$1.4783.
Ok, let's do the same trick with speed. Let's say I'm travelling at a constant speed so that: miles/hour = 60 Therefore multiplying each side by hours: miles` hours or to verbalise it: 1 mile is equivalent to 60 hours. which doesn't seem quite right does it?
It might help...
Suppose I want to create a graph of the cost of imported wheat compared with the dollar exchange rate. I put time in years along the bottom axis and the cost of wheat in £/tonne on the left axis - so far so conventional. Now I'm expected to put the value of the pound in £/\$ on the right axis but actually plot "The value of £1 divided by the value of \$1" Yes, that's very clear, very informative.
Thanks Thomas
Which is of course the inverse of how x/y would normally be read
Thomas