Understanding Significant Figures
Significant figures (often called "sig figs") are the digits in a number that carry meaning contributing to its measurement resolution. This includes all digits except:
- Leading zeros (e.g., 0.002 has 1 sig fig).
- Trailing zeros when they are merely placeholders (e.g., 1500 has 2 sig figs).
Rules for Identifying Significant Figures
To identify which digits are significant, apply these rules in order:
- Non-zero digits are always significant. (e.g., 1, 2, 3... 9).
- Any zeros between significant digits are significant. (e.g., 101 has 3 sig figs).
- Leading zeros are NOT significant. They only indicate the decimal point. (e.g., 0.0045 has 2 sig figs).
- Trailing zeros in a number containing a decimal point ARE significant. (e.g., 2.00 has 3 sig figs).
- Trailing zeros in a whole number with no decimal point are ambiguous. (e.g., 1500 could be 2, 3, or 4 sig figs depending on precision).
Rounding Significant Figures
When performing calculations, the result should not have more significant figures than the least precise measurement used in the calculation. To round to N significant figures:
- Identify the first N significant digits.
- Look at the (N+1)th digit.
- If the (N+1)th digit is 5 or greater, round the Nth digit up. Otherwise, leave it.
- Replace all digits after the Nth with zeros (if whole number) or drop them (if decimal).