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Significant Figures in Physics

How We Use Significant Figures in Physics

In our physics tutorials, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits, for example. If the input has fewer significant figures, the answer will also have fewer significant figures.

Care is also taken that the number of significant figures is reasonable for the situation posed. In some topics, particularly in optics, more accurate numbers are needed and more than three significant figures will be used. Finally, if a number is exact, such as the two in the formula for the circumference of a circle, \(c = 2 \pi r,\) it does not affect the number of significant figures in a calculation.

Check Your Understanding

Perform the following calculations and see if your answer using the correct number of significant digits corresponds to the answers provided.

(a) A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags?

(b) The force \(F\) on an object is equal to its mass \(m\) multiplied by its acceleration \(a.\) If a wagon with mass 55 kg accelerates at a rate of \(0.0255\;\text{m/s}^2,\) what is the force on the wagon? (The unit of force is called the newton, and it is expressed with the symbol N.)

Answers

(a) 37.2 pounds; Because the number of bags is an exact value, it is not considered in the significant figures.

(b) 1.4 N; Because the value 55 kg has only two significant figures, the final value must also contain two significant figures.

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