Overview
This lecture introduces standard and scientific notation, covering how to convert between them for large and small numbers, and how to correctly use scientific notation in calculations.
Standard Notation
- Standard notation is the usual way of writing numbers in everyday life, including decimals and commas.
- It can be cumbersome in science due to the need for many zeros for large or small values.
Scientific Notation Basics
- Scientific notation expresses numbers as a coefficient (between 1 and 10) times a power of 10.
- Powers of 10 use exponents; the exponent counts the number of zeros in the standard notation.
- Positive exponents (e.g., 10⁴) represent large numbers; negative exponents (e.g., 10⁻³) represent small numbers (fractions less than 1).
Writing Numbers in Scientific Notation
- Move the decimal after the first non-zero digit to form the coefficient.
- Count the number of decimal places moved; this is your exponent.
- Moving the decimal left gives a positive exponent; right gives a negative exponent.
- Examples:
- 70,9345 = 7.9345 × 10⁴
- 0.000411 = 4.11 × 10⁻⁴
- 306,000 = 3.06 × 10⁵
- 0.00884 = 8.84 × 10⁻³
- 2,760,000 = 2.76 × 10⁶
- 0.000000559 = 5.59 × 10⁻⁷
Entering Scientific Notation in Calculators
- Each calculator has a different method for entering scientific notation; check your calculator’s manual or online instructions.
- Practice entering and using scientific notation in calculations to avoid errors.
Key Terms & Definitions
- Standard Notation — the usual way numbers are written using digits and decimals.
- Scientific Notation — a way to write numbers as a coefficient (1-10) multiplied by a power of 10.
- Coefficient — the number between 1 and 10 in scientific notation.
- Exponent — the power of 10 indicating how many places the decimal is moved.
Action Items / Next Steps
- Practice converting numbers between standard and scientific notation.
- Read calculator instructions to learn how to enter scientific notation.
- Try entering and calculating with the example numbers for practice.