Measurement and Significant Figures

Humans use units of measurement to communicate experiences like distances and times. Some units are natural, while many, like length and mass, are arbitrary. When measuring, it's crucial not to overstate precision. We can only estimate one digit beyond the instrument's precision level. Any measurement will have significant figures (sig figs) which indicate its precision.

There are four main rules for determining significant figures: (1) Any non-zero digit is significant. (2) Zeros between non-zero digits are significant. (3) Leading zeros (before the first non-zero digit) are not significant. (4) Trailing zeros (after the last non-zero digit) are only significant if they are decimal zeros. For example, 10,000 has only one significant figure, meaning it's an estimate, not an exact value.

When performing calculations, pay attention to sig figs. For addition and subtraction, the answer should have the same number of decimal places as the value with the fewest decimal places. For multiplication and division, the answer should have the same number of significant figures as the value with the fewest sig figs. Always round the answer appropriately: 5 or higher rounds up, 4 or below rounds down.