Overview
This lecture explains the concept of significant figures (sig figs), why they matter in scientific measurement, and the rules for identifying and using them in calculations.
The Importance of Measurement and Precision
- Humans use measurements to communicate quantities and events.
- Some measurement units are based on natural phenomena, while others are arbitrary.
- Measurements are limited by the precision of our instruments.
Understanding Significant Figures (Sig Figs)
- Significant figures reflect the precision of a measured value.
- Only one digit should be estimated beyond the marked precision of the measuring device.
- Reporting more digits than the instrument's precision allows is incorrect.
Rules for Determining 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 the last non-zero digit) are significant only if they come after a decimal point.
Examples of Significant Figures
- 10,000 has one significant figure.
- 2.33 (measured value) has three significant figures.
- 2.33481 (for a less precise device) is not justified.
Calculating with Significant Figures
- When adding or subtracting, the result should have the same number of decimal places as the value with the least decimal places.
- When multiplying or dividing, the result should have the same number of sig figs as the value with the least sig figs.
- Round up if the dropped digit is 5 or greater; round down if it is 4 or less.
Key Terms & Definitions
- Significant Figures (Sig Figs) — The digits in a measurement that indicate its precision.
- Leading Zeros — Zeros before the first non-zero digit; not significant.
- Trailing Zeros — Zeros after the last non-zero digit; significant only if after a decimal.
- Precision — The level to which a measurement is exact.
Action Items / Next Steps
- Practice identifying significant figures in various numbers.
- Apply sig fig rules to sample addition, subtraction, multiplication, and division problems.