11.6: Currency Conversion

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The process of converting from one currency to the next is relatively simple, but can also be confusing. Because currencies quotations can be presented in two ways (direct vs. indirect quotes) it is not always easy to remember if you should multiply by the exchange rate or divide by the exchange rate. One way to keep this straight is through labels. For instance, let us say we need to convert $\$ 400$ US into British pounds. We know the exchange rate is 0.7280 pounds/dollar (an indirect quote). Since I want to know the value in pounds, I set this up as follows:
\[
(\$ 400)\left(\frac{0.7280 \text { pounds }}{\$ 1}\right)=291.20 \text { pounds }
\notag \]

Note that the " $\$$ " labels cancelled out with one in the numerator and one in the denominator, leaving me with pounds. What if I would have divided instead of multiplied?
\[
(\$ 400)\left(\frac{\$ 1}{0.7280 \text { pounds }}\right)=549.45 \$^2 / \text { pound }
\notag \]

Now, the dollars will not cancel out and I am left with "dollars squared/pound" which makes no sense. By leaving the labels in unless they cancel out, I can tell if I did my conversion correctly. This system will work for any currency conversion regardless of which direction I am converting (from foreign currency to US dollars or US dollars to foreign currency) or which quote format (direct or indirect) I am given.

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