Overview
This lecture explains scientific notation, its significance in handling very large or small numbers, methods for calculations, and key rules for operating with scientific notation.
Introduction to Scientific Notation
- Scientific notation expresses numbers as a digit term times an exponential term (e.g., 5.6 x 10⁻⁹).
- Useful for simplifying very large or very small numbers.
Structure and Examples
- Numbers are written as: digit term x 10^exponent.
- Positive exponents shift the decimal right; negative exponents shift it left.
- Only digits in the digit term count as significant figures; zeros for place-holding are not significant.
Calculating with Scientific Notation
- On scientific calculators, input the digit term, press EE/EXP, enter the exponent, and continue normal calculations.
- Non-scientific calculators require manual exponent calculations.
Rules for Operations
Addition and Subtraction
- Convert all numbers to the same power of 10, then add or subtract digit terms.
- Example: (4.215 x 10⁻²) + (3.2 x 10⁻⁴) = 4.247 x 10⁻².
Multiplication
- Multiply digit terms and add the exponents.
- Adjust result so one nonzero digit is left of the decimal.
- Example: (3.4 x 10⁶)(4.2 x 10³) = 1.4 x 10¹⁰.
Division
- Divide digit terms and subtract exponents.
- Example: (6.4 x 10⁶)/(8.9 x 10²) = 7.2 x 10³.
Powers and Roots
- For powers: raise the digit term, multiply exponents.
- For roots: take root of digit term, divide exponent by the root degree.
Key Terms & Definitions
- Scientific Notation — A format to write numbers as digit term x 10 to an exponent.
- Digit Term — The part showing significant figures.
- Exponential Term — The power of 10 expressing decimal placement.
- Significant Figures — The digits in a number that carry meaning in terms of accuracy.
Action Items / Next Steps
- Practice inputting scientific notation on your calculator.
- Complete the provided quiz questions for mastery.
- Review exponent manipulation rules for further understanding.