I live in Canada and all the street signs are posted in km/h and all my life I've been using metric. However, playing this game I prefer the units to be in US customary units (mph, HP, ft-lb) just because that's how I commonly hear them being expressed and it's more intuitive to hear that a Nascar stock is 850 HP than 634 kW.
My friend showed me a quick way to quickly estimate between miles and kilometers rather quickly using the Fibonacci sequence (which I found really cool because I'm a nerd like that).
http://en.wikipedia.org/wiki/Fibonacci_number
As the sequence progresses the ratio of two consecutive Fibonacci numbers approaches the irrational number phi which is approximately 1.618 (the proof of this requires quite a bit of math, so I'll just leave it out).
Now, 1 mile is approximately 1.6 km so this actually works out very nicely.
Example:
Say you're given a distance of 8 miles and you want to approximate the value in kilometres.
The first few values of the Fibonacci sequence are:
0, 1, 1, 2, 3, 5,
8,
13, 21, 34, 55, 98, 144...
Find
8 and notice that the next number in the series is
13.
Hence, 8 miles is approximately 13 km.
To go from kilometers to miles, just go the other way.
Now if you're given a value that's not a Fibonacci number, you can break that value into the sums of Fibonacci numbers and find each of its successors (to go from miles to km) or predecessors (to go from km to miles) and add them up.
For example, given 60 miles and you want to estimate it in kilometers.
Consider the sequence:
0, 1, 1, 2, 3,
5,
8, 13, 21, 34,
55,
98, 144...
Notice that 60 =
55 +
5
The successor of
5 is
8
and the successor of
55 is
89
The sum of
8 +
89 = 97
Hence, 60 miles is approximately 97 km.
Once again to go from km to miles, just work in the opposite direction of the series.