I am having a question regarding significant figures in calculating average of two masses. For example adding two masses 7 kg and 8 kg gives 15 kg, both inputs 7 and 8 have only one significant figure but final answer 15 has two significant figures.
Now if I take average of the masses 15/2 gives 7.5, (Note: the number 2 has infinite significant figures because it represent a whole quantity, so it is 2.0000… in actual)
Hence the calculated average 7.5 kg has two significant figures obtained from the sum 15 kg (which has 2 significant figures and it determines the significant figure of the result of division)
Is this logic correct? Can addition (or taking average) increase the significant figure of the result? Can I write my final average as 7.5 kg or should I write only 8 kg (after rounding off 7.5 to one significant figure because both inputs have only one significant figure)?
Thank you for your help in advance.
Best Answer
Consider what the number of significant figures indicates:
The number written as $7$ has $1$ significant figure; the number is somewhere between $6.5$ and $7.5$
The number written as $8$ has $1$ significant figure; the number is somewhere between $7.5$ and $8.5$
So, when you add these two numbers;$$7+8=15$$
the answer, $15$, lies somewhere between $6.5+7.5 =14$, and $7.5+8.5 =16$
$15 ± 1$ is not two significant figures...