Question about sig figs and rounding.

[Arnav]

Hey I just started taking a physics course and I am a bit confused about sig figs and rounding.

My question is that if there are two parts to a physics problem and the latter part requires an answer from the first part, then do you use the sig fig/ rounded value or the calculated value.

For example, you're solving for distance and you know initial velocity, final velocity and time. You use the formula
a = (vf - vi)/t

And then you use the formula
d = vi*t + 1/2 * a * t^2

When you substitute a (acceleration) in the second formula, would you use the sig fig/rounded value or the value that the calculator gives.

 

[pixel]

Best approach is to use the not-rounded-off acceleration value from the first equation that's in the calculator when evaluating the second equation. This is the same as just substituting the first equation into the second one and using just vi, vf and t to calculate d.

It's not too bad with just two equations, but if you had a series of equations, each of which carried over a result from the previous one and they were rounded off, the errors would compound. It all depends on how accurate the final result has to be.

 

[fresh_42]

In principle errors during a longer calculation add up, so it's always best to round at the end of a calculation. However, if your initial data are e.g. in hours and kilometers, it won't make much sense to carry seconds and meters through a calculation. A result can't be more accurate as the initial data. In my opinion it is good to be as precise as possible from the start and adjust only the final result. This might get you into trouble if the expected solution (at school) differs from your result, but hopefully not decisive. If in doubt, ask the teacher. In a research environment you need to keep track of the error margins in any case. It should be (an important) part of the experimental setup.