Often I am not sure when to make use of significant figures in a calculation.
For example at the moment. I have to calculate a certain equilibrium point which is given by:
$m^* = \frac{\phi_{\mathrm o}^{*2} A}{g K^2 A_{\mathrm v}^{*2}}$
And the values are: $\phi_{\mathrm o}^* = 0.001$, $A_{\mathrm v}^* = 0.001$, $\rho = 980$, $A = 1$, $K = 0.01$, $g = 9.81$. Now $m^* = 1.019367991845056e+03$
When applying the rules of significant figures the correct answer should be $m^* = 1e+03$, I believe. Since the amount of significant figures of the answer is equal to the number with the least amount of significant figures, which are $\phi_{\mathrm o}^*$, $A_{\mathrm{v}}^*$, $A$ and $K$, they all have 1 significant figure.
I am really questioning myself whether if I should use significant figures or not.
I hope some people can give some idea's/views when to use significant figures or not to use them.
Because $m^*$ is a equilibrium point I would say I would rather use $m^* \approx 1019.37$ rather then $1000$. But still one could argue also that I might use more digits, 1019.368.