Thank you for your reply. Your error is found at the beginning of your calculation: the exact marathon distance is not 26 miles + 385 yards. It is actually ever so slightly longer. To be precise, it is exactly 42.195 km.
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Wait, can you remind me how far exactly a marathon is again? It hasn't been well established in this thread yet.
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rekrunner wrote:
Looks like another argument to go metric.
But wait a minute.
Isn't the "exact" marathon distance 26 miles 385 yds?
In other words, exactly 26.21875 miles?
This makes the marathon distance exactly 42.194988 km
No rounding errors yet.
The popular metric approximation of 42.195 km is exactly 12mm too long.
12 mm is approximately -- rounded to 1000 significant digits:
0.0074564543068480076354092102123598186590312574564543068480076354092
10212359818659031257456454306848007635409210212359818659031257456454
30684800763540921021235981865903125745645430684800763540921021235981
86590312574564543068480076354092102123598186590312574564543068480076
35409210212359818659031257456454306848007635409210212359818659031257
45645430684800763540921021235981865903125745645430684800763540921021
23598186590312574564543068480076354092102123598186590312574564543068
48007635409210212359818659031257456454306848007635409210212359818659
03125745645430684800763540921021235981865903125745645430684800763540
92102123598186590312574564543068480076354092102123598186590312574564
54306848007635409210212359818659031257456454306848007635409210212359
81865903125745645430684800763540921021235981865903125745645430684800
76354092102123598186590312574564543068480076354092102123598186590312
57456454306848007635409210212359818659031257456454306848007635409210
212359818659031257456454306848007635409210212359818 miles.
iosonfrvuier wrote:
Don't forget the .01875745645430684800763540921. Anybody can do that for 26.2 miles, its the .01875745645430684800763540921 that gets you.
Nice try, but you're quoting more significant figures than you can be sure of. Yeah the maths still works but the physics has fallen apart. By the time you reach 37 decimal places you're talking about precision down to the exact number of atoms between 2 points.
If you want the real argument for metric, try converting between metres and kilometres compared with feet to miles in your head. Better still, lets see who's faster in multiplying 100m by 50 and expressing the answer in either kilometres or miles. We could do the same thing with weights if you want, and aside from familiarity with the scale, there is absolutely no argument for farenheit over celcius.
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When you look at the numbers 42.19488 and 42.195 -- these are accurate to an infinite number of significant figures. When you look at a conversion factor from km to miles, this factor is accurate to an infinite number of significant figures.When converting meters to miles, it is pure math. With two inputs of infinite precision, why should I be limited to some discussion of physics looking at distances at the atomic scale?
o11y217 wrote:
Nice try, but you're quoting more significant figures than you can be sure of. Yeah the maths still works but the physics has fallen apart. By the time you reach 37 decimal places you're talking about precision down to the exact number of atoms between 2 points.
If you want the real argument for metric, try converting between metres and kilometres compared with feet to miles in your head. Better still, lets see who's faster in multiplying 100m by 50 and expressing the answer in either kilometres or miles. We could do the same thing with weights if you want, and aside from familiarity with the scale, there is absolutely no argument for farenheit over celcius.
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