Perform the requested operations, propagate uncertainty. Report your answer in proper scientific notation, with absolute uncertainty.
[(3.4445 x 105) (± 0.035%)] / [(43.665) (± 6.2%)]
[(3.4445 x 105) (± 0.035%)] / [(43.665) (± 6.2%)] .
First the division of 3.4445E5/43.665 = 7.888E3 = y
s = y*sqrt[(0.00035/3.4445E5)^2 + (0.0062/43.665)^2]
then your answer is y from above +/- s from next to last line. Post your work if you get stuck.
My answer was 10.1611 when I need two numbers separated by the +/-. Can you explain in depth please?
When I simplified this: s = y*sqrt[(0.00035/3.4445E5)^2 + (0.0062/43.665)^2].
when you simplified that expression what did you get. I didn't go through the math. That value, when simplified is s
then the answer you want is y +/- s
That may be what your missing. Remember to put the answer in scientifi notation.
To perform the requested operations and propagate uncertainty, we need to follow certain steps:
Step 1: Convert the percentage uncertainty to decimal form by dividing it by 100. For example, 6.2% becomes 0.062.
Step 2: Determine the absolute uncertainty for each quantity by multiplying the value by its corresponding percentage uncertainty. For example, for (3.4445 x 10^5), the absolute uncertainty would be (3.4445 x 10^5) x (0.035/100) = (1.20358 x 10^2).
Step 3: Calculate the result by dividing the values and dividing the absolute uncertainties. The result will be reported in scientific notation.
Now, let's perform the calculations:
[(3.4445 x 10^5) ± (1.20358 x 10^2)] / [(43.665) ± (43.665 x 0.062)]
The result is:
[7.885112403 ± 0.076161120] x 10^3
Therefore, the final answer, in proper scientific notation with absolute uncertainty, is (7.885112403 ± 0.076161120) x 10^3.