Suppose you are an engineer, and you are asked to measure the force on a supporting beam of a bridge.

F = (500 ± 4) 10² lb

Explanation:

This is an exercise in the uncertainty or error of a measurement.

If a single measurement is made, the way to give the result is the measurement value plus the appreciation of the instrument that corresponds to the absolute error, in the form

           F = x ± Δx

For this, a suitable uniform is the use of scientific notation, where each magnitude is written with an integer and some decimals multiplied by an exponential.

           X = 50067 lb = 5.0067 10⁴ lb

the uncertainty is

           Δx = 400 lb = 4.00 10² lb

so the result for the report must be written

          F = (500 ± 4) 10² lb

where the significant figures are adjusted to the measurement error.

In the case of making a series of measurements, the value obtained is the average of the measurements and the error must be given by the standard deviation