Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. They're essential in scientific calculations, measurements, and data reporting.
Rules for Counting Significant Figures
- All non-zero digits are significant
- 123 has 3 sig figs
- 45.67 has 4 sig figs
- Zeros between non-zero digits are significant
- 1002 has 4 sig figs
- 50.03 has 4 sig figs
- Leading zeros are NOT significant
- 0.0045 has 2 sig figs (only 4 and 5)
- 0.00012 has 2 sig figs (only 1 and 2)
- Trailing zeros after the decimal ARE significant
- 12.300 has 5 sig figs
- 1.0 has 2 sig figs
- Trailing zeros before the decimal may or may not be significant
- 1200 could have 2, 3, or 4 sig figs (ambiguous)
- Use scientific notation to clarify: 1.2×10³ (2 sig figs)
How to Round to Sig Figs
- Count from the first non-zero digit
- Count the required number of significant figures
- Look at the next digit to determine rounding direction
- Round up if it's 5 or greater, down if less than 5
Worked Example
Round 45.678 to 3 significant figures:
- Count 3 sig figs from the left: 45.678
- Look at the 4th digit: 7
- Since 7 ≥ 5, round up
- 6 becomes 7
- Answer: 45.7
Common Uses
- Scientific Research: Reporting measurements with appropriate precision
- Chemistry Labs: Calculations with measured values
- Physics Problems: Maintaining precision through calculations
- Engineering: Specifications and tolerances
- Data Analysis: Presenting results with justified precision