[B9766]

I'm getting mixed signals from my text book and professor regarding the determination of significant digits in a combination addition and multiplication problem.
I have no problem understanding straight forward multiplicationision and addition/subtraction.
However, in a problem like:
$$x = (25.335*124.25)+(1.0749*0.00301)=3147.876985$$
Should the answer be 3150. due to 0.00301 having only 3 significant digits or should it be 3147.88 due to 124.25 only having 2 decimals?
(assume none of the factors are constants)

[Borek]

Should the answer be 3150. due to 0.00301 having only 3 significant digits or should it be 3147.88 due to 124.25 only having 2 decimals?

Neither.

Rules for products and sums are a bit different. There are two products and a sum. Results of the products are 3147.87375 - of which only five digits matter (as there are five digits in 124.25), and 0.003235449 - of which only 3 digits matter. Now, when you try to add these numbers and write them one under another, aligning decimal points:

3147.87375
   0.003235449


you will see the lower number is completely irrelevant, as it is added to non-significant digits of the much larger first number. So the final answer is just 3147.9

Don't worry too much about significant digits, you will probably never use them outside of the course. Serious work requires serious methods of error propagation calculation, significant figures are rather useless in this context.

[B9766]

Thanks Borek. I followed that. I'm taking Chem I, again, after 50 years. This time I'm more interested in the why than the how. I appreciate you taking the time to explain.