Video Transcript
If the relative error in measuring
an area of 320 meters squared was 0.03, calculate the absolute error for that
measurement.
In this question, we’re asked to
determine the absolute error of a measurement if we know the relative error. First, let’s remember that relative
error is a way of showing the error proportional to the accepted value. We can recall that the equation for
relative error is given by 𝑟 equals Δ𝑥 over 𝑥 zero, where 𝑟 is the relative
error, Δ𝑥 is the absolute error, and 𝑥 zero is the accepted value.
Now let’s make the absolute error
Δ𝑥 the subject. We can do this by multiplying both
sides of the equation by the accepted value 𝑥 zero to give us Δ𝑥 equals 𝑟
multiplied by 𝑥 zero. We are told in the question that
the relative error is equal to 0.03, which is a dimensionless number, so 𝑟 is equal
to 0.03. The accepted value of the area is
320 meters squared. So 𝑥 zero is equal to 320 meters
squared.
We can now substitute in the given
values into the equation to find that the absolute error Δ𝑥 is equal to 0.03
multiplied by 320 meters squared. This gives us an answer of 9.6
meters squared, and this is the correct answer. The absolute error for this
measurement is 9.6 meters squared.
