Overview
This lecture covers how to express numerical measurements in chemistry using standard and scientific notation, focusing on converting between them and understanding exponents.
Standard Notation
- Standard notation is the usual way to write numbers, including decimals and commas (e.g., 25, 18,000).
- Large or small numbers in standard notation can be unwieldy due to many zeros.
Scientific Notation
- Scientific notation expresses numbers as a coefficient (between 1 and 10) multiplied by a power of 10.
- The format is: coefficient × 10^exponent.
- For large numbers, the exponent is positive and equals the number of decimal places moved left.
- For small numbers (less than 1), the exponent is negative and equals the decimal places moved right.
Steps to Write Scientific Notation
- Place the decimal after the first nonzero digit to create the coefficient.
- Count how many places the decimal was moved (left = positive, right = negative exponent).
- Multiply the coefficient by 10 raised to the appropriate exponent.
Examples of Scientific Notation
- 70,9345 becomes 7.9345 × 10⁴.
- 0.000411 becomes 4.11 × 10⁻⁴.
- 306,000 becomes 3.06 × 10⁵.
- 0.00884 becomes 8.84 × 10⁻³.
- 2,760,000 becomes 2.76 × 10⁶.
- 0.000000559 becomes 5.59 × 10⁻⁷.
Using Scientific Notation on Calculators
- Calculators have various methods for entering scientific notation; check your calculator’s instructions.
- Practice using your calculator to enter and manipulate numbers in scientific notation for accuracy.
- Store each step in the calculator before multiplying by the next value.
Key Terms & Definitions
- Standard Notation — the regular way numbers are written in daily life.
- Scientific Notation — a shorthand format: coefficient × 10^exponent.
- Coefficient — the number (between 1 and 10) in scientific notation.
- Exponent — the power of 10, showing how many places to move the decimal.
Action Items / Next Steps
- Practice converting numbers between standard and scientific notation.
- Find and review your calculator’s method for entering scientific notation.
- Complete any assigned problems using the examples provided.