Add $( 9.2 \times 10^3 \textrm{ s}) + (8.3 \times 10^4 \textrm{ s}) + (0.008 \times 10^6 \textrm{ s})$.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. To make sense out of the significant figures in our answer here, it helps to convert this scientific notation, I mean although strictly speaking, this one here is not in scientific notation but anyway to change this times 10 to the power of business into a standard notation which is what you call these numbers here, helps to figure out what the significant figure should be in our answer. So we have 9.2 times 10 to the 3 is 9200 and this 0.008 times 10 to the 6 is we'll move this decimal point six points to the left, one, two, three takes it to the 8 there and then three more times gives you these three zeros and then here's our answer 100200 but that's not our final answer. When you are adding numbers, your answer will be as precise as the least precise number that you used in your addition. So both of these numbers have a tie for being the least precise; they are both precise only to the thousands place—the 3 and the 8 here. This number here—9200—is precise to the hundreds place but that's not gonna matter because we are gonna look at the numbers that have the worst precision which both of these numbers take a tie for being precise only to the thousands place and so that means our answer will be precise only to the thousands place which is here. And so our final answer then is 1.00 times 10 to the one, two, three, four, five and normally, we'd put units on a number like this but there are no units in this question. So 1.00 times 10 to the 5 is our answer with the correct significant figures.