Math
Master the quantitative skills used in science and healthcare: significant figures, unit conversions, proportions, functions, exponents, logarithms, statistics, and introductory calculus.
Significant Figures
Sign in to track progressSignificant figures (sig figs) express the precision of a measured or calculated value. Using the correct number of sig figs prevents over-reporting precision in any scientific calculation.
Counting Significant Figures
- All non-zero digits are significant.
- Zeros between non-zero digits are significant.
- Leading zeros (before the first non-zero digit) are NOT significant.
- Trailing zeros after a decimal point are significant.
- Trailing zeros in a whole number without a decimal are ambiguous unless written in scientific notation.
Examples:
- 45.6 has 3 sig figs
- 0.0045 has 2 sig figs (leading zeros are not significant)
- 2005 has 4 sig figs
- 0.200 has 3 sig figs
- 200 (without decimal) is ambiguous
Significant Figures in Multiplication and Division The result should have the same number of sig figs as the measurement with the fewest sig figs.
Example: 2.5 × 3.42 = 8.55 → round to 8.6 (2 sig figs)
Decimal Place Rules for Addition and Subtraction The result should be rounded to the same number of decimal places as the measurement with the fewest decimal places.
Example: 12.34 + 1.2 = 13.54 → round to 13.5 (1 decimal place)
Rounding Calculations Correctly
- If the digit after the last kept digit is 5 or greater, round up.
- If it is less than 5, keep the last digit unchanged.
- Carry extra digits through intermediate steps and round only at the final answer.
Key Points
- Non-zero digits and captive zeros are always significant
- Leading zeros are never significant; trailing zeros after a decimal are significant
- Multiplication/division results match the least number of sig figs
- Addition/subtraction results match the least number of decimal places
- Round only the final answer to avoid compounding rounding errors