You do the math
Stephen here again (Anne seems to be a reluctant blogger). We’re starting to think in dollars a bit more now, rather than converting everything to sterling. Anne’s managing to make the change a bit better than me. When we talk about the price of something I still often append it with “…that’s about X pounds”.
Now we’re earning Aussie dollars, and given that we plan to be here for about eight months in total, I really should try to stop doing this.
So how to change the currency you think in? The first thing to do is to gauge the price of staple goods. For example:. a cup of steaming hot Joe (coffee). We did this by looking at a few coffee shops and finding out the price of a standard “flat white” (that’s what they call a white coffee – or white americano – here). We included in this survey Starbucks and McDonalds, to give our benchmarking exercise an upper and lower limit. From then on we didn’t need to convert the price of a coffee as we could quickly gauge if it was reasonable or not. And whether we could afford cake to go with it.
For items we don’t buy regularly conversion to sterling can still be helpful. The conversion rate is about 2.8 dollars to the pound. We found this a bit difficult at first, and the mathematician in me didn’t like the rough “divide by three” method as the would be 6.7% (to 1d.p.) lower than the actual figure, and so we’d be convincing ourselves things were cheaper than they were.
And so we figured out an algorithm using what we called “Numerical Analysis” at uni. Our improved method was to divide by three and then add 10%. This was much better as it over-estimated the sterling amount, but only by 2.7% (to 1 d.p.). That’s a 60% reduction in the magnitude of the systematic-error, and an overestimate rather than an underestimate, which is preferable.
The accountant in me is happy with this as he considers a 2.7% error to be immaterial. Especially given that 2.8 dollars to the pound was the rate when we left the UK, and that could well have moved by now!
Let’s see an example of this in practice:
Example 1.1
Stephen wants a slice of almond and cherry pie, which costs $3. How can Stephen tell how much this is in sterling, given that he can’t divide by 2.8 in his head, and doesn’t own a cool calculator-watch because Anne said the look stupid and he wasn’t allowed one?
[You may say that Stephen can easily see quite quickly that the cake would be just over a pound, but that gross simplification neglects to remember that Stephen is a boring accountant and therefor requires an answer in pounds and pence.]
Let’s put our algorithm into practice:
3 divided by 3 is 1. Add 10% to 1 and you get 1.1. Therefore the delicious almond and cherry slice is 1 pound and ten pence (overstated by 2.7%). (Sorry – no pound sign on these silly, silly keyboards.)
Stephen buys the cake, happy now he knows how much it would cost in sterling to with 2.7% (barring any transaction costs of exchange, and movement in the exchange rate in the last seven weeks). The attractive, comely serving-wench smiles alluringly at him as she takes his money, not realising that Stephen has a beautiful girlfriend and therefore hasn’t even noticed this girl’s Cameron Diaz-esque good-looks and barely-covered body.
You see – who said foreign travel was difficult? Next time you go abroad be sure to take with you an accountant/mathematician and a scientist. The fun and laughter will be never-ending.
I hereby grant permission to anyone who is thinking about writing a maths text book to use my real-life example of applied maths.