value of pi and 22/7

[Ethan Furman]

On 06/17/2016 06:19 PM, Steven D'Aprano wrote:
> On Sat, 18 Jun 2016 09:49 am, Ian Kelly wrote:

>> If I tell you that the speed of light is 300,000,000 m/s, do you think
>> that measurement has 9 significant digits? If you do, then you would be
>> wrong.
>
> Hmmm.
>
> 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?

I know!  I know!  9!

> What if I tell you that it's 300,000,001 m/s?

Oh!  9 again!

> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

Hmmm... thinking.... thinking... oh yeah!  You put a bar over the last 
significant digit -- or you use scientific notation:

30e7 has two significant digits.

> For all that it is in widespread use, I think the concept of "significant
> figures" is inherently ambiguous.

Not at all -- just have to keep your notations correct*.

--
~Ethan~

* Mine might be 30 years out of date, but maybe not.