Meaning of significant figures in chemistry
Significant figures (sig figs) communicate the precision of measured quantities in general chemistry. A reported value includes all certain digits plus one estimated digit. The sig fig rules ppt summary below organizes the counting rules, rounding rule, and calculation rules that control how many digits may be reported in a final result.
Sig fig rules ppt (slide-style cheat sheet)
- Nonzero digits are significant.
- Leading zeros (zeros before the first nonzero digit) are not significant.
- Captive zeros (zeros between nonzero digits) are significant.
- Trailing zeros are significant only if a decimal point is present (or if significance is stated via scientific notation).
- Exact numbers (counted objects, defined conversion factors) have infinite significant figures and do not limit rounding.
- Rounding: look at the first dropped digit; if it is \(\ge 5\), increase the last kept digit by 1; if it is \(<5\), keep it unchanged.
- × or ÷: result has the same number of significant figures as the factor with the fewest significant figures.
- + or −: result has the same number of decimal places as the term with the fewest decimal places.
Counting significant figures
| Number | Sig figs | Reason (rule) |
|---|---|---|
| 0.00450 | 3 | Leading zeros not significant; trailing zero after decimal is significant: 4, 5, 0. |
| 1002 | 4 | Captive zeros significant (between nonzero digits). |
| 1500 | 2 (ambiguous) | Trailing zeros without a decimal point may be placeholders; clarify with scientific notation. |
| 1.500 × 103 | 4 | Scientific notation states significance explicitly. |
| 12 (students) | Unlimited | Counted objects are exact. |
Calculation rules with worked examples
Multiplication / division (fewest sig figs)
Example: density \( \rho = \dfrac{m}{V} \) with \(m = 12.3\ \text{g}\) and \(V = 4.56\ \text{mL}\).
\[ \rho = \frac{12.3}{4.56} = 2.697368\ldots\ \text{g/mL} \]The factors have 3 sig figs (12.3) and 3 sig figs (4.56), so the result is reported with 3 sig figs: \( \rho = 2.70\ \text{g/mL} \).
Addition / subtraction (fewest decimal places)
Example: \( 23.47\ \text{mL} + 1.8\ \text{mL} + 0.006\ \text{mL} \).
\[ 23.47 + 1.8 + 0.006 = 25.276\ \text{mL} \]The fewest decimal places among the terms is 1 (from 1.8), so the sum is rounded to 1 decimal place: \( 25.3\ \text{mL} \).
Mixed operations and guard digits
For multi-step problems (stoichiometry, gas laws, calorimetry), carry extra digits during intermediate steps (guard digits) and round only at the end using the correct rule for the final operation. Intermediate rounding can shift the last digit and degrade accuracy.
Visualization: decision flowchart for sig fig rules
Note on “ppt” units
If “ppt” is used as a concentration unit (often “parts per thousand” in some contexts), the same significant figure rules apply: the number of reported digits in the ppt value must match the measurement precision and the rounding rule of the calculation that produced it.