I'm confused about significant digits in multi-step problems. If I have something like (7.004 +0.2230)/(15.1-0.033+12.07) do I first do the addition and round to 4 sig figs and then do the denominator and round to 2 sig figs and finally divide? Or do I just work everything out and wait till the very end to round? Please help!

Do the additions in the numerator and denominator separately, and round the results to the largest significant decimal place in the sum. The numerator would be 7.227 and the denominator would be 27.1.

Then do the division and keep three significant digits, which is determined by the accuracy of the denominator.

I get 0.267, but I'm sloppy at math. See what you get.

Thanks a lot. I think it's great what you teachers do on this site. Very generous of you all to help us out.

Thank you for your kind words. We can't help everyone, but we try. It's fun to help students understand how to do the problems themselves. Teachers and textbooks are often unclear.

When performing multi-step calculations involving significant figures, the general rule is to carry out all calculations first, and then round the final answer to the appropriate number of significant figures.

In your example, you would first perform the addition (7.004 + 0.2230) and get 7.227. Then, you would perform the subtraction (15.1 - 0.033 + 12.07) and get 27.137. Finally, you would divide the sum (7.227) by the difference (27.137), resulting in a quotient of approximately 0.266.

Now, when it comes to determining the number of significant figures in the final answer, you need to consider the least precise measurement or value used in the calculation. In this case, the least precise value is the denominator (27.137) with three significant figures. Therefore, you would round your answer to three significant figures, giving you 0.266.

To summarize, the correct approach is to perform all intermediate calculations without rounding and then round the final answer to the appropriate number of significant figures based on the least precise value used in the calculation.