# 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

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: $$3.0 \times 1.0 = 3.0$$ $$3.0 \times 1 = 3$$ $$3,472 \times 12 = 42,000$$ $$2 \times 2.075 = 4$$