I have long been confused with significant digits for questions that involve acombinationof addition / subtraction & multiplication / division, in science classes I have lost marks frequently on this, I know the calculations but I lost marks on roundings...so frustrated...I really need an expert on this to help me out...I would really appreciate because I am going to take Physics in which significant digits is particularly important!

Q1:The speed of P waves is 6.8 km/s and the speed of S waves is 4.1 km/s. How long would it take P waves and S waves to travel 100 km respectively?

This is simple!

t(P waves)=d/v

=100/6.8 (3 significant digits divided by 2 significant digits)

=14.7 sec (unround answer)

=15 sec (2 significant digits as a final answer to this question)

Similarily,

t(S waves)=d/v

=100/4.1 (3 significant digits divided by 2 significant digits)

=24.4 sec (unround answer)

=24 sec (2 significant digits as a final answer to this question)

Q2:What is the lag time between the arrival of P waves and S waves over a distance of 100km? (lag time is the time difference in arrival times of P waves and S waves)

I am starting to get confused...

Lag time=t(S waves) - t(P waves)

=(100/4.1) - (100/6.8)

=24.4 - 14.7 (use unrounded intermediate answers from above)

=9.7 or 9 or...? (problem starts to arise here...this calculation of lag time involve a combination of division and subtraction, some possible rounding methods popping off my head:

(i) (100/4.1) - (100/6.8) involve a combination of division and subtraction so it just follow the "rule of number of significant Digits in multiplication & division", i.e. the number of significant digits in an answer should equal the least number of significant digits in any one of the numbers of measurement, in this case, 2 significant digits, thus the final answer is 9.7 sec

(ii) 24.4 - 16.4 both have 1 deciminal place so the final answer should have 1 deciminal place as well, ie 9.7 sec

(iii) Follow "rule of number of significant Digits in multiplication & division" when doing the when doing multiplication/division and also follow "rule of number of significant Digits in addition & subtraction" when doing addition/subtraction, that is, rounding off every step:

=(100/4.1) - (100/6.8)

=24 (2 significant digits) - 15 (2 significant digits)

Now, doing subtraction and both have 0 deciminal place

Thus the final answer is 9 sec (0 deciminal place)

(iv) other...

Can someone point out the correct number of significant digits or deciminal places that should be in the final answer of Q2 and explain why?

Q3:Given the lag time for Austin is 150 sec, the distance from Austin to the location of the earthquake can be found using this formula:

distance = [lag time for Austin (s) x 100 km ] / [lag time for 100 km (s)]

The unrounded answer is 1546.3918 km, again I don't know how many significant digits I should keep in the final answer because I don't know the number of significant digits to the answer of Q2.

Thank you again for helping!