Significant digits in calculation

[php006]

Hello everyone:
I am trying to figure out the how many significant figures (sf), should I keep in the final
answer for multiplication and division
1. How many hours and minutes are 20 kiloseconds?



2.



3. for hours: 20*10e3 / 3600 = 5.5555 hrs
20 has only 1 significant figure (trailing zero doesn't count), hence the answer should have 1 sf, that means I should round answer to the single digits. my final answer is 6 hr. My book give 5.6 hr as the answer.
please let me know my approach is correct

for minutes 20*10e3 / 60 = 333.333 minutes
keep only 1 sf in the result,that leads my answer to 333 minutes
my book give 330 and the final answer

 

[Ouabache]

Your book appears to be choosing 2 significant digits. However you could just as well choose 3 sf and still be correct. I would state what I'm using for sf, in my solution. To 3 sf, hours would be 5.56hr. If you see the answer in your book as 5.6hr, you should realize, both answers are correct.

 

[Blueshift5]

should be 330 min

I would like to clarify that the number of significant figures (sf) in a calculation depends on the number of significant figures in the numbers being used in the calculation. In multiplication and division, the final answer should have the same number of sf as the number with the least sf. In this case, 20 has only 1 sf, so the answer should also have 1 sf. Therefore, the answer for the first question should be 6 hours, not 5.6 hours as given in your book.

Similarly, for the second question, since 20 has 1 sf, the answer should also have 1 sf. Therefore, the answer for minutes should be 330 minutes, not 333 minutes as calculated by you. It is important to note that the final answer should be rounded to the nearest significant figure, not the single digit.

I hope this clarifies your doubts and helps you understand the concept of significant figures in calculations. It is important to be consistent and accurate in using significant figures in scientific calculations as they represent the precision of the measurement and can affect the accuracy of the final result. Thank you for your question and keep up with your scientific inquiries.