My wife and I are memorizing certain things together and some will have distances, for example the average distance of certain objects in space from the sun. We live in the United States where most people uses miles. (I’ve always been a proponent of switching to the metric system.) So we’ve been talking about if we should remember distances in miles or km. We don’t want to remember both. We plan on learning mental math as well so my question is would it be easier to convert miles to km by multiplying the distance number by 1.609 or to convert km to miles by dividing the distance by 1.609 using mental math. Is it even reasonably possible? (You may be asking yourself why I don’t round to 1.6 and it’s because I want better accuracy.)
I don’t know the answer to your question, but it seems like multiplying would be easier.
I remember 5:8 and then divide by one or the other, but it isn’t highly accurate. 
150 kilometers is just under 100 miles.
150 / 8 is about 19, and 19 * 5 = 95 miles
(actual 93.2057)
25 kilometers / 8 is about 3.
3 * 5 is 15 miles
(actual 15.5343)
Other direction:
72 miles / 5 is about 14.
14 * 8 = 112 kilometers
(actual 115.873)
Which way to remember distances, kilometers or miles? You’re in the United States, and people are going to give you distances in miles. Use miles. Saint Ambrose said it best, “When in Rome, do as the Romans do.”
Is an error margin of 5.625 miles for every 1000 miles really essential to your calculations? If so, just use 1.6 to multiply, and then add 5.625 for every 1000 miles in the answer. If you know the first few multiples of 56 (56, 112, 168, 224, 280), this shouldn’t be difficult.
Other easy methods for converting kilometers to mile:
The “good enough” military version:
miles to km - divide the number by 6, and move the decimal one place to the right.
km to miles - multiply by 6, and move the decimal one place to the left.
(This is actually equivalent to multiplying by 1.66666.)
The bit-by-bit method:
miles to km - Take the number of miles, and add half of that, then add the original number of miles with the 1s digit removed. For example: 50 miles = 50 (original miles) + 25 (half of that) + 5 (original number of miles with 1s digit dropped) = 80 km
(This is equivalent to multiplying by 1.6.)
The Fibonacci version:
Break the number of units up into a sum of Fibonacci numbers, then…
miles to km - …replace each Fibonacci number with the next Fibonacci number, and work out the new sum.
km to miles - …replace each Fibonacci number with the previous Fibonacci number, and work out the new sum.
(This works because it’s a simple means of multiplying by phi, which is roughly 1.61803399…)
You could also perform both the bit-by-bit method and the Fibonacci method, and then average the 2 answers. This is equivalent to multiplying by 1.609016994374947424102293417182819058860154589902881431067…