value of pi and 22/7

[Tim Harig]

On 2016-06-18, Steven D'Aprano <steve at pearwood.info> 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.
> What if the figure to nine significant digits *actually is* three followed
> by eight zeroes?

The you can either write it as 300000000. (notice the trailing decimal
indicating that all of the zeros are indeed significant) or write it it
scientific notation.

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

Only for those who do not understand it.

The main problem I have with significant figures is that measurement
accuracy is often not constrained to a decimal system.  A scale that can
measure in 1/5 units is more accurate than a scale that can measure only
in whole units but it is not as accurate as a scale that can measure
all 1/10 units.  Therefore it effectively has a fractional number of
significant figures.

I could just cut my loses and express the lower number of significant
figures but, I usually express the error explicitly instead:

<measurement> +- 0.2 units

where +- looks like the ± html entity.