how do i figure out the percentage error , as well as the absolute error of
a) (10.00+/- .02)mL x .42 mol/L
b) (10.00 +/- .02)mL + (10.00 +/- .02)mL
thanks in advancee plz help
a) The % error is 0.02/10 = 0.2%
The absolute error is 0.2% of the product. The product is 4.2*10^-3 mol Take 0.2% of that for the absolute error.
b) The errors, being supposedly random, add as the square root of the sum of the squares. The result is 20.00 +/- 0.028. That is 0.14% relative error.
for b where do u get the =/e .028?
and what about the absolute error?
I already stated the absolute error in (b).
As I said before, 0.028 is the square root of the sum of two 0.02's squared.
It is possible that your teacher wants you to add the absolute errors, and not take the square root of the sum of the squares. To do so would give you an overly conservative worst case error. Errors should be handled statistically.
Refer to
http://en.wikipedia.org/wiki/Mean_squared_error
To calculate the percentage error and absolute error in these cases, we need to understand the formulas for each.
1. Percentage error:
Percentage error is a measure of how inaccurate a measurement is compared to the actual value. It is calculated using the formula:
Percentage error = (Absolute error / Actual value) × 100%
The absolute error is the difference between the measured value and the actual value.
2. Absolute error:
Absolute error represents the magnitude of the difference between the measured value and the actual value, without considering its direction. It is calculated as:
Absolute error = |Measured value - Actual value|
Let's calculate the percentage error and absolute error for each scenario you mentioned:
a) (10.00 +/- .02)mL x .42 mol/L
Step 1: Calculate the absolute error:
Absolute error = |10.00 mL - Actual value|
Step 2: Calculate the percentage error:
Percentage error = (Absolute error / Actual value) × 100%
To proceed, we need to know the actual value that we are comparing the measurement against. Please provide the actual value to continue the calculation.
b) (10.00 +/- .02)mL + (10.00 +/- .02)mL
Step 1: Add the measured values:
Measured value = 10.00 mL + 10.00 mL
Step 2: Calculate the absolute error:
Absolute error = |Measured value - Actual value|
Step 3: Calculate the percentage error:
Percentage error = (Absolute error / Actual value) × 100%
Again, we need the actual value to proceed with the calculations. Please provide the actual value to complete the calculation.