[philonossis]

"A football team has the following distribution of players:
- 22.0% are defensive linement with an average mass of 271 lb.
- 19.0% are defensive backs with an average mass of 175 lb.
- 26.0% are offensive linemen with an average mass of 263 lb.
- 15.0% are offensive backs with an average mass of 182 lb.
- 19.0% are specialty team members with an average mass of 191 lb.

What is the average mass of a football player in this team?"

This problem is meant illustrate how a weighted average of isotopic masses is determined.

Methodology: The book states: "To find the weighted average we
(1)multiply each distinct value by its fractional abundance, that is by it percentage expressed in decimal form,
(2)and then we sum the products from the multiplications."

All the multiplications have 3 sig figs, e.g., .220 x 271 = 59.6. This would mean that when the addition is done, sig figs would be to the amount of least uncertainty, i.e, to the 10ths place.

 Multiply average mass by percentage:
(22.0% =) .220 x 271 lb = 59.60 (three sig figs = 59.6)
(19.0% =) .190 x 175 lb = 33.25
(26.0% =) .260 x 263 lb = 68.48
(15.0% =) .150 x 182 lb = 27.30
(19.0% =) .190 x 191 lb. = 36.29


If I set the calculator to give me multiplications answers with 3 sig figs, that gives 59.6, 33.3, 68.4, 27.3, and 36.3.  The sum of these is 224.9. But the book answer is 224.8

If we round the first multiplication answer to 59.6 but keep all the others at their calculator answers (two decimal places) and then round them after adding, we get 224.8200000. Rounding to the 10ths place, the place of least uncertainty (59.6) we get 224.8.

I don't understand where the rounding is supposed to take place in this procedure because the answer differs depending on when it is done.

I hope someone might be able to clarify if the book or I am wrong here. and where the rounding happens.

[sjb]

I don't understand where the rounding is supposed to take place in this procedure because the answer differs depending on when it is done.

I hope someone might be able to clarify if the book or I am wrong here. and where the rounding happens.

Usually what I do is round right at the end, so I would be adding in this case 59.60.. + 33.25.. + 68.48.. etc, then rounding as a final step.

[Biopolmonkey]

As above, I was always taught only to round the final answer.