Find the absolute and percent relative uncertainty and express each answer with a reasonable amount of significant figures.
9.2(+ or -0.7)*(0.0054(+-0.3)+0.0056(+-0.7)
The Algebraic answer: 0.1012
Absolute error?
Relative error %?
Step 1: Use order of operations, multiplication before addition. Percent uncertainty is required for multiplication, %e=sqroot((0.7/9.2)*100)^2+(0.3/0.0054)*100)^2)
step 2: Now add the two numbers together, using absolute uncertainty for addition e=sqroot((your number from the previous calculation)^2+(0.7)^2)= gives your absolute uncertainty.
Step 3: To find percent uncertainty from absolute uncertainty simply divide your percent uncertainty by your final algebraic answer * 100
To find the absolute error, you need to find the maximum possible difference between the algebraic answer and the upper and lower bounds of the measurements.
For the upper bound:
Upper bound = (9.2 + 0.7) * ((0.0054 + 0.3) + (0.0056 + 0.7))
Upper bound = 9.9 * (0.305 + 0.305)
Upper bound = 9.9 * 0.61
Upper bound = 6.039
For the lower bound:
Lower bound = (9.2 - 0.7) * ((0.0054 - 0.3) + (0.0056 - 0.7))
Lower bound = 8.5 * (-0.295 + (-0.694))
Lower bound = 8.5 * -0.989
Lower bound = -8.4
Absolute error = [(Upper bound) - (Lower bound)] / 2
Absolute error = [(6.039) - (-8.4)] / 2
Absolute error = 14.439 / 2
Absolute error = 7.2195
To find the relative error percentage, you need to divide the absolute error by the algebraic answer and then multiply by 100.
Relative error % = (Absolute error / Algebraic answer) * 100
Relative error % = (7.2195 / 0.1012) * 100
Relative error % = 71.4137 * 100
Relative error % = 7141.37%
Therefore, the absolute uncertainty is 7.2195, and the percent relative uncertainty is 7141.37%.