Rounding error?

Question

Mathematics

I decided to repeat school mathematics
I study Skanavi, there is an example
"Determine the absolute error that occurs when replacing an irrational number (root of 3) = 1.73205508 ...
with its approximate value of 1.73
Solution:
We have a0 = 1.7320508 ..., a = 1.73. Replacing the exact number a0 by its approximate value a, we make the following error: |(root of 3) - 1.73| = 0.0020508...
It is clear that in the case under consideration we can put (delta a0) = 0.003 (number (delta a0) in accordance with the accepted condition written with one digit and obtained by rounding the error 0.0020508... upwards)
"
Help me understand where they got 0.003 from, how does this rounding up happen?

Answer 1

It's just the author's mistake. But it's not scary. The term "error" after the introduction of GOST R ISO 5725-1-2002 completely left the science of measurements (metrology), where it comes from. Now there is accuracy, which in turn includes correctness (which used to be systematic error) and precision (which was previously random error).

Answer 2

Rounding up is just
1. We have some number, 0.0020508...
2. We chose the number of decimal places to round up to
(the author wanted to leave only one significant number, that is, in this case, 3 decimal places)
3 We discard all the remaining digits, we got 0.002 - this number turned out to be less than the original one, so we take a little higher, 0.003

Answer 3

usually
1 2 3 4 are rounded to zero
5 6 7 8 9 - to one
in Python, by the way, its round() five also to zero, this is a well-known feature / bug / xs that
but you can round anything, any way and anywhere
that the root of 3 may well be equal to both two and one, depending on the conditions and IRL
, so in the condition they wrote you "increasing"
why - because we are looking for abs, that is, the maximum error
for the model to fit into the door, being increased by a million times
times in the direction of increase, then
1 2 3 4 5 6 7 8 9 - all in
1,205 you become 300
, that's all. There is no absolute. There is either a default (-4 - zero, 5 - one), or a condition (all in one)

Answer 4

0.003

is precision. You can't round up. it is necessary in the nearest) Here the author takes the confidence interval, which must include the real value of the physical quantity.
In short, +-0.25 cannot be written as +-0.2, because it will be a lie. But can be written as +-0.3 (or +-0.9/+-20).