- #1
012anonymousx
- 47
- 0
A position of a particle in linear motion is given by:
x = vt + 0.5at2
Calculate x with the error for:
t = 25.3 ± 0.5s
v = 10.1 ± 0.4m/s
a = 2.5 ± 0.3m/s2
So for calculating vt:
q = (10.1) (25.3) = 255.53 (exact)
Δq = (10.1)(25.3) * √ (0.4/10.1)2 (0.5/25.3)2
= 11.31...
Therefore, vt = 255.53 ± 11.3 (the 11.3 is rounded because I heard uncertainties always rounded to precision of last uncertainty)
Now my question is:
How do you round 255.53? And how many sig figs?
Is it 260.0 ± 11.3?
Or 255.5 ± 11.3?
OR something else?
And why?
I thought 260.0
Because when there is just a number to a certain position with no uncertainty given, like 123.4 it is implied that:
123.4 ± 0.1
So the number is rounded to the lowest precision of the uncertainty (I think)
(i.e. if the uncertainty was ± 0.12, the rounding would still occur at the 10th decimal place.
In this case the tenth decimal place.
In the case of 255.53 ± 11.3, it is the 10's.
Therefore 260.0
I'd appreciate if someone would type of a full solution (doesn't have to be pretty).
I guess a similar question is let's say you have the number
1234.5678 +/- 123.45
How should 1234.5678 be rounded?
x = vt + 0.5at2
Calculate x with the error for:
t = 25.3 ± 0.5s
v = 10.1 ± 0.4m/s
a = 2.5 ± 0.3m/s2
So for calculating vt:
q = (10.1) (25.3) = 255.53 (exact)
Δq = (10.1)(25.3) * √ (0.4/10.1)2 (0.5/25.3)2
= 11.31...
Therefore, vt = 255.53 ± 11.3 (the 11.3 is rounded because I heard uncertainties always rounded to precision of last uncertainty)
Now my question is:
How do you round 255.53? And how many sig figs?
Is it 260.0 ± 11.3?
Or 255.5 ± 11.3?
OR something else?
And why?
I thought 260.0
Because when there is just a number to a certain position with no uncertainty given, like 123.4 it is implied that:
123.4 ± 0.1
So the number is rounded to the lowest precision of the uncertainty (I think)
(i.e. if the uncertainty was ± 0.12, the rounding would still occur at the 10th decimal place.
In this case the tenth decimal place.
In the case of 255.53 ± 11.3, it is the 10's.
Therefore 260.0
I'd appreciate if someone would type of a full solution (doesn't have to be pretty).
I guess a similar question is let's say you have the number
1234.5678 +/- 123.45
How should 1234.5678 be rounded?