I'm really embarrassed to ask this! I knew how to do it before but I forgot after 2 years. I remember learning it for analytical chemistry :(
So a basic problem:
What is x= a+b+c?
given that:
a= 100.7 +/- 0.05
b= 0.61 +/- 0.005
c=226 +/- 0.5
OK. My question is the following:
I understand the answer is
x = 327.31 +/- 0.5025186564...
HOWEVER, I have no idea how the sig figs go.
Do I treat each part "separately?" And by part, I mean the thing before the +/- and the thing after. If I do that, then the part before is 327 and the thing after is 0.5..... is my answer than 327 +/- 0.5??? It looks incorrect :(
To summarize my messy post, I am unsure how to write my final answer
Don't worry, I'm here to help! When dealing with significant figures, we need to follow certain rules to determine the number of significant figures in a calculated result.
In your case, to determine the number of significant figures in the final answer for x, you should consider the following rules:
1. Addition/Subtraction: When adding or subtracting numbers, the final result should have the same number of decimal places as the number with the fewest decimal places in the original values.
Looking at your given values, "a" has two decimal places, "b" has three decimal places, and "c" has no decimal places. So, to maintain the correct number of decimal places in the final result, we should consider "c" to have two decimal places (since it has the fewest). Therefore, the sum of a, b, and c would be 327.31 (keeping two decimal places).
2. Uncertainty/Error Propagation: To determine the uncertainty or error in the final result, we need to consider the maximum possible error from the given values.
For addition or subtraction, we sum up the absolute uncertainties. In this case, the absolute uncertainties are 0.05 for a, 0.005 for b, and 0.5 for c. Adding them up, we get 0.555.
Considering significant figures, round the uncertainty to the same decimal place as in the result. Since our result has two decimal places, we round the absolute uncertainty to 0.56 (keeping two decimal places).
Thus, the final answer for x becomes:
x = 327.31 +/- 0.56
Therefore, your earlier understanding was correct. The answer is x = 327.31 +/- 0.56, considering two significant figures provided by the values and following the rules for addition/subtraction and uncertainty propagation.