Overview
This lecture covers the principles and steps for expressing numbers in scientific notation, with a focus on clarity, significant figures, and notation rules.
Introduction to Scientific Notation
- Scientific notation eliminates ambiguous zeros and clearly indicates significant figures.
- Only one nonzero digit appears to the left of the decimal in scientific notation.
- Place value is shown by multiplying by a power of 10.
Converting to Scientific Notation
- Move the decimal after the first nonzero digit.
- Drop ambiguous or placeholder zeros that are not significant.
- The power of 10 equals the number of decimal places moved:
- Moving decimal left: positive exponent (large to small number).
- Moving decimal right: negative exponent (small to large number).
Examples
- 130,000 → Move decimal 5 places left: 1.3 × 10⁵.
- 0.00000499 → Move decimal 7 places right: 4.99 × 10⁻⁷.
- For numbers with significant zeros (e.g., zeros between other digits or after decimal points), keep all significant digits in your answer.
- Always count and preserve all significant figures when converting to scientific notation.
Significant Figures in Scientific Notation
- Zeros between nonzero digits and zeros at the end of a decimal are significant.
- Scientific notation retains all significant digits; there is no rule limiting the number of significant figures.
- For example, 230.0 (with 4 sig figs) → 2.300 × 10².
Key Terms & Definitions
- Scientific Notation — A format for writing numbers with one digit left of the decimal and a power of 10 for place value.
- Significant Figures — Digits in a number that carry meaning regarding its precision.
- Ambiguous Zero — A zero whose significance is unclear (placeholder vs. measured).
- Power of 10 — The exponent representing how many places the decimal was moved.
Action Items / Next Steps
- Write down the word "Vader."
- Prepare for the next lecture.