Mechanics

calculus-based physics for scientists and engineers

Significant Figures

How to Find the Number of Significant Figures

The number of significant figures represents how precisely a number is known. Check out the table.

NumberSignificant Figures
322
32.59406
325,9405
320,0002
320,000.07
0.00000322
0.03203

Clearly, significant figures would be simple if it were not for the zeros! However, do the following to find the number of significant figures.

  1. The first significant figure is the non-zero digit furthest to the left.
  2. Continue counting to the right.
  3. Is there a decimal point?
    • Yes: continue counting to the last digit of the number.
    • No: continue counting only to the last non-zero digit.

That's it!

Significant Figures and Computations

When doing calculations, follow these rules to determine the significant figures of your answers.

  1. For multiplication, division, and taking roots the result will have the same number of significant figures as the input number with the least number of significant figures.
  2. For addition and subtraction, the last significant figure in the result has the place value of the input number whose last significant figure has the largest place value.
Input Result
3.0 x 1.0 3.0
3.0 x 1 3
3,472 x 12 42,000
2 x 2.075 4

See these two rules in action: $$ 3.0 \times 1.0 = 3.0 $$ $$ 3.0 \times 1 = 3 $$ $$ 3,472 \times 12 = 42,000 $$ $$ 2 \times 2.075 = 4 $$

Exercises

Do Now!   Do these exercises immediately.

Not Now!   Do these after you start to forget the topic, say in a week.

More!   More exercises if you want. Maybe review before a test.

Required Problems

Optional Problems