6) How many significant figures should be retained in the result of the following calculation?
12.00000 x 0.9893 + 13.00335 x 0.0107
A) 2
B) 3
C) 4
D) 5
I thought it was 3, but it is 4. Can you please explain to me
You should have used parentheses.
If the number is as I have divided it up.
(12.00000 x 0.9893) + (13.00335 x 0.0107)
then 12.000 x 0.9893 = 11.8716 and we can keep 4 places. Round that to 11.87.
Now 13.00335 x 0.0107 = 0.13914, then add them. We can keep two places to the right and no more; therefore, we have 4 places; i.e., the
11.87
0.14
------
12.01
noobs at significant figures .
Jon is correct with his thinking, but Dr. Bob222 is correct. You should do this in steps to see why.
(12.00000 x 0.9893) + (13.00335 x 0.0107)
Jon is correct. With multiplying numbers the number with the least number of Sig figs determines how many Sig figs are in the answer. In this case, 4 Sig for the left side of the equation.
12.000 x 0.9893 = 11.87
Again, Jon is correct. 3-Sig figs for the other side of the equation.
13.00335 x 0.0107 = 0.139
This is why Jon is wrong. When adding your answer has to be rounded to a place that has no more uncertainty then the individual numbers to be added that has the least amount of uncertainty. In this case, 11.87 has the least amount of uncertainty compared to 0.139.
11.87 + 0.139=12.009= 12.01. ===>four sig figs.
To determine the number of significant figures that should be retained in the result of the given calculation, you need to follow the rules for significant figures.
1. Rule for multiplication or division: The result should have the same number of significant figures as the measurement with the fewest significant figures.
In the given calculation, 12.00000 has 6 significant figures and 0.9893 has 4 significant figures. So, the calculation involving these two numbers should retain 4 significant figures.
2. Rule for addition or subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
In the given calculation, 13.00335 has 5 decimal places and 0.0107 has 4 decimal places. So, the calculation involving these two numbers should have 4 decimal places.
Now, let's perform the calculation:
12.00000 x 0.9893 + 13.00335 x 0.0107
= 11.8716 + 0.1394981
= 12.0110981
Since we determined that the multiplication should have 4 significant figures and the addition should have 4 decimal places, the final result should also have 4 significant figures.
Therefore, the correct answer to the question is C) 4.