Overview
This lecture reviews how to determine the significance of zeros in numbers and how to handle significant figures in multiplication and division calculations.
Rules for Zero Significance
- Zeros sandwiched between non-zero digits are significant.
- Zeros to the right of non-zero digits without a decimal point are not significant.
- Zeros to the right of a non-zero digit with a decimal point are significant.
- Leading zeros (zeros to the left of a non-zero number) are not significant.
Multiplication and Division with Significant Figures
- When multiplying or dividing, round the answer to the fewest significant figures among the numbers used.
- After calculating, keep only the required number of significant figures and replace other digits with zeros if necessary.
- Always check if rounding is needed by examining the next digit to the right.
Example Calculations
- 307 (three significant figures) × 32,000 (two significant figures) = answer rounded to two significant figures.
- A number with four significant figures (zeros to the right and decimal present) × another with three significant — round final answer to three significant figures.
- In division: five significant figures ÷ two significant figures = answer rounded to two significant figures.
- Multiplying 0.0005 (one significant figure) × a three-digit number (three significant) = answer rounded to one significant figure.
- 0.0xyz... (ignore initial zeros), count sandwich or decimal zeros when identifying significant figures.
Key Terms & Definitions
- Significant Figures (Sig Figs) — the digits in a number that carry meaning, including all non-zero digits, sandwiched zeros, and zeros to the right of a decimal after a non-zero digit.
- Leading Zeros — zeros appearing before all non-zero digits; not significant.
- Trailing Zeros — zeros at the end of a number; significant only if there is a decimal point.
Action Items / Next Steps
- Practice significant figure rules with additional multiplication and division problems.
- Review textbook examples on identifying significant digits, especially involving zeros.