Overview
This lecture explains how to determine significant figures in scientific notation and how to handle significant figures during calculations involving addition, subtraction, multiplication, and division.
Determining Significant Figures in Scientific Notation
- Ignore the 10 raised to a power (exponent) when counting significant figures.
- The part before the exponent (mantissa) determines the number of significant figures.
- All nonzero digits and zeros to the right of a decimal in the mantissa are significant.
Multiplication and Division Rules
- Perform the operation on the mantissas first, ignoring the 10 to the power part.
- Round the result to the least number of significant figures present in the mantissas.
- For exponents, add (multiplication) or subtract (division) the exponents as separate steps.
- Adjust the final number to correct scientific notation: one nonzero digit before the decimal.
- Moving the decimal right decreases the exponent by one; moving left increases it by one.
Addition and Subtraction Rules
- Exponents must be the same before adding or subtracting numbers in scientific notation.
- Add or subtract the mantissas, keeping exponents unchanged.
- Round the result based on the fewest decimal places in the original mantissas.
- Adjust the final answer to proper scientific notation if necessary, changing the exponent accordingly.
Key Terms & Definitions
- Scientific Notation — A way to express very large or small numbers as a product of a mantissa and a power of ten (e.g., 5.42 × 10¹⁹).
- Mantissa — The decimal part of a number in scientific notation, which determines significant figures.
- Significant Figures — The digits in a number that carry meaningful information about its precision.
Action Items / Next Steps
- Practice solving scientific notation problems, applying the rules for significant figures in calculations.
- Review rounding rules for addition/subtraction and multiplication/division with significant figures.