What is precision of a number representation? (was: Curious Omission In New-Style Formats)

[Ben Finney]

Ethan Furman <ethan at stoneleaf.us> writes:

> I will readily admit to not having a maths degree, and so of course to
> me saying the integer 123 has a precision of 5, 10, or 99 digits seems
> like hogwash to me.

Precision is not a property of the number. It is a property of the
*representation* of that number.

The representation “1×10²” has a precision of one digit.
The representation “100” has a precision of three digits.
The representation “00100” has a precision of five digits.
The representation “100.00” also has a precision of five digits.

Those can all represent the same number; or maybe some of them represent
“one hundred” and others represent “one hundred and a millionth”.

The representation is only an approximation of the actual number, and
the precision tells us how fuzzy the approximation is.

None of these say how *accurate* the representation is; if those are
representations of the number “seven thousand” they are not very
accurate, while they might be passably accurate for the number “one
hundred and seventy”.

> But I'm always willing to learn.  So please explain what 123 with a
> precision of five integer digits means, and what to do we gain by
> saying such a thing?

We gain clarity of speech: we distinguish the different aspects (how
many digits of this representation are actually claimed to represent the
number?) communicated by a representation.

-- 
 \        “… no testimony can be admitted which is contrary to reason; |
  `\   reason is founded on the evidence of our senses.” —Percy Bysshe |
_o__)                        Shelley, _The Necessity of Atheism_, 1811 |
Ben Finney