What answer should be reported, with the correct number of significant figures, for the following calculation:
(965.43 x 3.91) + 9413.4136
I got 13189 as an answer. Can someone let me know if this is right?
the answer is 13180.
you do what is in parenthesis first and round it 3sf and get 3770 and then add 9413.4... and then round to least number of decimal places so you would get 13180
To determine the correct number of significant figures in the answer, we need to consider the significant figures in the given numbers and follow the rules of significant figures in calculations:
Given:
965.43 (5 significant figures)
3.91 (3 significant figures)
9413.4136 (7 significant figures)
The first step is to perform the multiplication:
965.43 x 3.91 = 3778.8913
Next, add the result to 9413.4136:
3778.8913 + 9413.4136 = 13192.3049
To round the final answer to the correct number of significant figures, we count the significant figures in the original numbers being added.
The number with the fewest significant figures in the original calculation is 3.91, which has three significant figures. So, we round the answer to three significant figures.
The final answer, with the correct number of significant figures, is:
13192.3049 = 13200
Therefore, the answer should be reported as 13200.
To determine the correct answer with the appropriate number of significant figures, we need to consider the significant figures in the given numbers and in the calculation itself.
Starting with the given numbers:
- 965.43 has five significant figures.
- 3.91 has two significant figures.
- 9413.4136 has ten significant figures.
For multiplication, the rule is to count the smallest number of significant figures in the factors involved, which in this case is two. Therefore, the product of 965.43 and 3.91 should be rounded to two significant figures. Performing this multiplication, we get:
965.43 x 3.91 ≈ 3776 (rounded to two significant figures)
Now, adding this result to 9413.4136:
3776 + 9413.4136 = 13189.4136
Lastly, we round the final result to match the least number of significant figures among the given numbers, which is two. Rounding 13189.4136 to two significant figures, we obtain the final answer:
13189.4136 ≈ 1.3 x 10^4
Thus, the correct answer with the appropriate number of significant figures is 1.3 x 10^4.