It's both easier and more accurate to multiply by 1.6
Yes. 1.6 = (1 + 0.5 + 0.1).
So just halve the number and add it to itself. Need more accuracy add 10%.
A mathematician's way of converting miles to kilometers
171–180 of 208 posts
Re: A mathematician's way of converting miles to kilometers
#172Earlier quoted context omitted.
In base 8 (if we'd had 8 fingers), an "order of magnitude" would have been defined as "times 8" instead of "times 10", so it would also be adding another 0. Same with base 12. Base 16 would have the further advantage that we could easily halve, quarter, eighth, or 16th any number ending in 0 to a whole integer (in base 10, we can only halve, fifth, or tenth).
> In base 8 (if we'd had 8 fingers) Seven fingers. Base 11 is the natural base for a ten fingered person: Base 11 has a distinct symbol for ten, base 10 does not. [A prime base has quite a few practical disadvantages... and their advantages are fairly esoteric...]
I mean it's not so bad. If we meet aliens there is a decent chance that they will have a base-9 counting system in balanced ternary: so their digits would be -4, -3, -2, -1, 0, 1, 2, 3, 4. Rather than prefixing negatives with a minute sign, maybe negation would flip a number top-to-bottom.
Re: A mathematician's way of converting miles to kilometers
#173Earlier quoted context omitted.
What if we had just 4 digits on each limb or even 6 perhaps. How does those numbers look in base 8 or 12.
I never bought this argument, but I'm not confident about it. Isn't base 10 inherently intuitive because of the obvious reasons? IE an order of magnitude is just another 0? Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10…
You are correct that "10" is a very special number, as long as you don't assume that it can only mean "ten".
In fact, every number base is base "10" when you interpret the "10" in that base.
Try it:
10 binary is two.
10 octal is eight.
10 hexadecimal is sixteen.
This is the very definition of a number base: it is the multiplier that you represent by appending "0" to a string of numeric characters in that base.
So that is where the fundamental and special nature of "10" comes from; it's not because it happens to mean "ten" in our customary number base.
Ten is nothing special, "10" is. "10" is simply the way you write N where N is whatever number base you're working in. It's just as special in every number base!
p.s. I'm sorry you were downvoted so heavily for asking an honest question. You can't be the only one who has wondered about this, and your question led to an interesting discussion.
Re: A mathematician's way of converting miles to kilometers
#174I basically just use 6. 1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6. Instead of multiplying by 1.6 you would divide by 0.6, which basically amounts to dividing by 6 and then moving the decimal point to someplace plausible.…
Multiplying by 1.6 is the same as adding 0.6, so the calculation going to KM is about the same either way.
For whatever reason, six tenths and add is mentally quicker for me than division.
Re: A mathematician's way of converting miles to kilometers
#175As a programmer, I am much more facile with powers of 2, than Fibonacci. My way is to double the number 4 times (multiplying by 16) and divide by 10. So for example 55 mph, double 4 times: 110, 220, 440, 880 divide by 10: 88 So 55 mph is approximately 88 km/h
This is so brilliant! As a runner (most distances in running are measures in meters) and a programmer, this is just perfect! Thanks for sharing!
Re: A mathematician's way of converting miles to kilometers
#176As a programmer, I am much more facile with powers of 2, than Fibonacci. My way is to double the number 4 times (multiplying by 16) and divide by 10. So for example 55 mph, double 4 times: 110, 220, 440, 880 divide by 10: 88 So 55 mph is approximately 88 km/h
Good trick. A little easier: divide by 10 first and then double four times.
Re: A mathematician's way of converting miles to kilometers
#177I just remember that an inch is 2.54 cm, exactly (unless it's a "survey inch"), and there are 12 inches in a foot, and 3 feet in a yard ... but then I get stuck remembering how many yards there are in a chain and how many chains in a furlong.
Re: A mathematician's way of converting miles to kilometers
#178If you know your powers of two
1, 2, 4, 8, 16, 32, 64, 128, 256, 512
1, 128, 16, 2, 256, 32, 4, 512, 64, 8
32 miles is 51.2 kilometers
80 miles is 128 kilometers (wrap around!)
Re: A mathematician's way of converting miles to kilometers
#179Earlier quoted context omitted.
Fahrenheit to Celsius: (100F -30)/2= 35C
Not quite. It is 37.78. In temperature couple of degrees means a lot.
For outside temperatures it's close enough though. As an American who travels to Central America quite a bit being about to do: (C*2) + 30 to get F is close enough.
Re: A mathematician's way of converting miles to kilometers
#180I basically just use 6. 1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6. Instead of multiplying by 1.6 you would divide by 0.6, which basically amounts to dividing by 6 and then moving the decimal point to someplace plausible.…
>1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6.
How about just 1.5 + 0.1? I.e. the same amount plus half, plus a tenth?
So, 55 mi -> 55 + (25 + 2.5) + 5.5 -> 88km
And inversely, 0.5 + 0.1, so half plus a tenth:
80km -> 40 + 8 -> 48 miles
And for most purposes, just (one and a half = 1.5) and (half = 0.5) is close enough. You can mentally add a little more.
So
55mi -> 55 + (25 + 2.5) -> 82 (let's say around 85)
80km -> 40miles (let's say around 45 miles)