Question

How do errors are propagated or combined

Answer 1

Errors are propogated or combined when you do operations like multiplication, division, addition or subtraction on values with errors.

Consider 2 values,
25±1 and 20±2, where 1 and 2 are errors respectively.
For addition and subtraction, errors are added.
That means,
25±1 + 20±2 =45±3
and
25±1 - 20± 2= 5±3

For multiplication and division, we add relative errors.
For a= 25±1 , relative error is 1/25
For b= 20±2, relative error is 2/20.
So, when you multiply both numbers, the relative error in result will be sum of relative errors
Let z=a×b
relative error in z= (Δz/z) = ±((1/25)+(2/20))

When multiplying by real numbers, just multiply error by the number.
Eg: 2×(20±2)=40±4