# Exchange rates - is my math correct here?

Using an online exchange rate calculator, and Numi (a calculator that does it as if it's written by hand, for Mac OS X) for my calculations, it says:

1 GBP in USD = \$1.32

1 USD in GBP = £0.76

Is this the correct calculation:

A car costs \$54,600 USD but what would it cost in British Pounds if it were sold here?

My calculation:

54,600 USD * 0.76 GBP = £41,496

54,600 USD / 1.32 GBP = £41,363

The GBP is the denominator here, am I correct?

and:

A car costs £54,600 GBP but if it was sold in the U.S. what would it cost, roughly:

£54,600 * 1.32 = \$72,072 USD

The USD is the denominator here, am I correct?

Are my calculations correct, or am I wrong with the basic math of exchange rate about when to multiply or divide?

Multiply to find USD, divide to find GBP from USD?

You can use the units as helper in many calculations, if you look at them and use them properly:

In your example, you used 1.32 as the conversion ratio, that would be 1.32 USD per GBP = 1.32 USD/GBP.

If you now calculate with units: 54600 USD / (1.32 USD / GBP) =41363 GBP, your result will have GBP as unit, which shows you did it the right away.

If you did it wrong: 54600 USD * (1.32 USD / GBP) = 72072 USD^2/GBP, you end up with USD squared divided by GBP, which shows you it was wrong.

This method is very useful throughout any mathematical or especially physics calculations

In addition to the correct answer of Aganju, it should be noted that one or both of these conversion factors has been rounded off, lessening the accuracy of the results.

If the factor of 1.32 is exact, then the exact reciprocal factor should be 0.757575...

The rounding-off of the conversion factor leads to the inconsistency in the example in the OP. Multiplying by one factor or dividing by the other factor should give exactly the same result; not the 133 GBP difference seen in the OP.

If the exact conversion factor is used:

54,600 * 0.757575... we get 41,363.36, the same as the result from dividing by the other factor.

Additionally, you will never see exact reciprocal rates in use. You cannot change, for example, US\$ into Canadian\$ at one bank, walk across the street to another bank and change them back to get exactly the same US\$. Someone pays for the bank employees. buildings, advertising, etc...

• Or, looked at another way, the GBP/USD rate only has only 2 significant figures (less than the 3 for the USD/GBP rate), so one wouldn't generally expect the two calculations to match any better than that, which they don't. Using 3 significant figures for both (1.32 and 0.758), gives results that match to 3 significant figures. – Rick Goldstein Apr 29 at 14:30