How often to round sf in multi-step calculations

Jonathan Zuo 2J
Posts: 35
Joined: Fri Sep 25, 2015 3:00 am

How often to round sf in multi-step calculations

Lets say the problem gives you the wavelength of some type of light (2.69x10^-9) and wants you to find the energy of this light. You would first find the frequency of this light source by using $c=\lambda \nu$. When you do the math and get the frequency of the light, do you round it to 3 significant figures right away and then solve for energy using $E=h\nu$ or do you use the unrounded answer in your calculator and plug that into $E=h\nu$?

Tiffany Chen 2E
Posts: 26
Joined: Fri Sep 25, 2015 3:00 am

Re: How often to round sf in multi-step calculations

Personally, for a problem like this, I would actually rearrange the equation c=λv into v=c/λ and then plug the rearranged equation into E=hv for v in order to avoid any rounding errors. However, if you were to do it with multiple steps, my TA actually told me to round the first answer at least 2 sig figs beyond the needed amount (in this case you would round to 5 sig figs) and then plug that into E=hv for your final answer.