Use the Fibonacci sequence. Cool math trick: Converting between miles and kilometers | MNN - Mother Nature Network
Here's one I figured out a few years back, to convert mpg (US) to liters per 100 km's: divide either value into 235.2.
I'd see that as cooler if it seemed easier than other methods, but are you planning to (a) memorize the Fibonacci sequence up to 144 or so, or (b) work it out in your head up to the number you need, just in order to get an answer that's sort of intriguingly close, but not right? If you're converting kilometers to International Statute Miles, multiplying by 15625 then dividing by 25146 is exact, by the definitions of the two units. (There's only one kilometer, but a few different miles in use; that won't be exact for other flavors of mile.) If approximate is ok and you don't want to multiply/divide by five-digit numbers, you can't beat 1006 / 1619 in four digits, or 535 / 861 in three digits, or 23 / 37 in two digits, or 5 / 8 in single digits. Those are progressively more approximate, but even the last is only inexact by about 0.6 percent. -Chap
5 / 8 is the goodest you can do if you only want single-digits to multiply and divide by. Next worse after that is 3 / 5, and then 2 / 3. Errors: 0.6% for 5/8, 3.4% for 3/5, 7.3% for 2/3. Going in the other (better) direction, error for 23/37 is 0.04%, for 535/861 is 0.001%, for 1006/1619 is 0.000004%, and of course 15625/25146 is exact. -Chap
I really wish they hadn't "burned their bridges" when they established the metric measurement system, made it some easy/exact conversion factor. But no, they had to use some lightwave, or line of latitude/longitude, common everyday stuff right. Decades in Canadian engineering and steel detailing firms, you wouldn't believe the malarkey and palaver conversion caused.
Air Canada had the famous "Gimli glider" incident when they accidentally loaded the wrong Kg of jet fuel onto the aircraft, related to the Canada conversion to metric. Boeing 767 ran out of fuel at 40,000 ft, but the pilots knew how to fly gliders so they glided it down to defunct air field now used as Gimli raceway.
In Britain, our speedos had both mph and km/h on them, so you generally just know what is what. And conveniently, as someone who lives in Australia and has British clients, the exchange rate between the pound and the Aussie Dollar has been just about exactly the mph to kmh ratio for most of the past year, so I can generally do the conversions in my head. (Although as someone who has some clients who pay in pounds, I preferred it when it was 2 to 1.)
I picked that one up not quite a decade ago. Really impressed an acquaintance across the border when it lead to an almost instant mental conversion. (It shouldn't have, 47 divides into that super easy.) Long I ago I finally memorized the exact conversion factor, 1.609344, which matches your 25146/15625. That would have been after several years of deriving it from an easier exact ratio, 1 inch == 2.54 cm. And that later exact ratio seemed so much easier to remember than the other common approximation, 1 meter ~= 39.37 inches. Why memorize a 4 digit approximation, when a 3 digit exact ratio is available? At least you actually look at those, and get a feel for it. Too many folks here don't. Such as a former car pool partner, who complained about a speeding ticket in Canada. How could she know what the conversion was? Then she was so embarrassed when we showed her the km/h ring on her speedo. ... and a PC member trying to force a NHTSA recall of a certain Prius model that lacks both measures.
i have no idea what that link was talking about. i just google the conversions, including language. (although, there is sometimes more than one answer)
When I was a kid in Britain, we'd get weather forecasts in F and C as well, so these days I have those conversions in my head too (but only up to about 90F, because it never gets hotter than that in Britain). Your car pool partner is a genius. When I lived in Hong Kong, one of my friends bought a used 911. He test drove it on a Sunday; every Sunday night, my wife and I would meet him and his wife and a few other friends in a pub on the beach near our house. He was incredibly enthusiastic about this car. He said, "You know some cars just feel fast? This one really did. Honestly, when I was doing 100, it felt like I was doing 160. It was amazing. I had to dodge a lot of very slow traffic on the motorway, though. Bloody Sunday drivers." He said he needed to get it checked, to make sure there were no hidden faults, but that if it was all OK, he would definitely buy it. So he got it tested by an independent inspector at the HKAA. The report said that the engine, suspension, brakes, electronics and bodywork were all perfect. The only problem was that it was a UK import and the speedo was in MPH; it would have to be converted to km/h to be legal in HK. That kind of explained why it felt so fast. Like with your friend, I'm not sure how he missed the inner ring, but there you go.
I can't memorize Fibonacci numbers, but I can multiply by decimal point in my head. From miles to kilometer multiply by 1.6 From kilometer to miles multiply by 0.62 But I mostly rely on this. Unit Converter - Android Apps on Google Play
The simpler the better, I say! After all, when it comes to imagining distance in your mind just how accurate do you need to be? I can't imagine to more than one or two decimal places of distance myself and I'd be very surprised if anyone could except for very short measures.