if we multiply 2x24 = 48
and if we take the decimal digits for example 2.08 x 24 = 49.92
Now which answer is correct or both answers are correct?
Now if the unit is km so the error is too big 1.92 km. ohhhh it is horrible!!
If i look carefully to uncertainty measure and error i see we have to move on and not care too much.
What do you think about these digits and uncertainty value?
It all depends what you are measuring and how much error is acceptable. In measuring nuclear diameter you use fermi, whereas diameter of earth few thousand Km whereas distance of sun from earth light year. So different units in different domains. (Think just reverse --->1cm + - 1 km (totally unreasonable).
it is not uncertainty it is a numerical error and you can Eliminate the error whit numerical methods .
For that reason we look for the relative error of rounding:
100*(2.08-2)/2.08 = 3.846154 (%)
Do you think a ~4% error is negligible?
The problem of evaluation of the desired accuracy in specification of physical quantities could be resolved adequately only in the framework of dimensional analysis. The essence of the approach used in this discipline is described succinctly in the following quote:
"Science begins with the observation and precise description of things and events. It is at this very first step that we face the fact upon which dimensional analysis rests: Description in absolute terms is impossible"
End quote
For further information please consult the following reference
http://web.mit.edu/2.25/www/pdf/DA_unified.pdf
Angles don't have dimension and have an upper limit. It would be interesting if there were (often) an absolute uncertainty. Then, Galton's board and its probability distribution would be easier to understand.
And in science with modeling and simulation, the complex composed calculations contain dependency on several functions, but actual values and +- is not used. They are linearised and not reduced, because it could/must depend on a number of things?
It would be less correct reducing them, or keep nonlinearities and make conclusions from that?
It all depends what you are measuring and how much error is acceptable. In measuring nuclear diameter you use fermi, whereas diameter of earth few thousand Km whereas distance of sun from earth light year. So different units in different domains. (Think just reverse --->1cm + - 1 km (totally unreasonable).
Angles are defined as a ratio of lengths which both scale according to the same reference unit. Some authors suggest that the angle should be considered as a dimensionless unit
http://www-personal.umich.edu/~dsbaero/library/DimensionalAnalysisHarish.pdf
The force screw or a helix are fundamental and there, an inplane angle is connected to the out-of-plane dimension through the elevation.
they are both correct, 2*24=48 and 2.08*24=49.92, it's up to the precision of your measure which one you can use. If your measure is 2 u can use only the first one, if your measure is 2.08 you have to use the second one. Of course the result is influenced by the precision u have in establishing your measure, either 2 or 2.08 or 2.1.
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