value of pi and 22/7

Christian Gollwitzer auriocus at gmx.de
Sat Jun 18 03:56:42 EDT 2016


Am 18.06.16 um 03:19 schrieb Steven D'Aprano:
> If I tell you that some physical phenomenon [let's call it the speed of
> light] is 299,999,999 m/s, how many significant digits would I be using?
>
> What if I tell you that it's 300,000,001 m/s?
>
> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

You can't read off the number of significant figures from a value 
itself, it must be given as a side information. It is a common way to 
indicate uncertainty estimes, however, by giving a number to as many 
decimal places as there are significant digits, i.e. to indicate the 
uncertainty as a power of ten. You need to use exponential notation to 
express that clearly, in that case:

	3*10^8 -> (3 +/- 0.5) * 10^8
	3.0 *10^8 -> (3.0 +/- 0.05)*10^8

For more accurate error estimates, the second notation is used. Another 
common way to express this is something like

	3.42(3) which means 3.42 +/- 0.03

Note, however, that in current SI units the speed of light is known exactly:

	c = 299,792,458 m/s

There is no error! This is possible because the unit metre is defined by 
this value from the unit second.

	Christian


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