Jun 6, 2024

**Numbers and Measurements**: Reflect our knowledge about a physical object or entity in the real world.**Uncertainty in Measurements**: All measurements, whether taken by an instrument or manually, have a degree of uncertainty. This depends on the device used.**Estimated Digit**: The last recorded digit is usually an estimated digit, marking the point where certainty ends and estimation begins.

- Different instruments provide different levels of certainty.
- Example: Two balances may provide different degrees of certainty for the same object.
- Simple balance: certainty runs out in the tenths place.
- Precise balance: certainty goes down to the thousandths place.

- Significant figures give us an idea of the level of uncertainty in a measurement.

**Non-Zero Digits**: Always significant.- Example: 213.5 has 4 significant figures.

**Leading Zeros**: Not significant.- Example: 0.0023 has 2 significant figures (2 and 3).

**Trailing Zeros**: Significant if they are to the right of the last non-zero digit and to the right of the decimal place.- Example: 19.3400 has 6 significant figures.

**Captured Zeros**: Zeros between two significant figures are significant.- Example: 13.6009 has 6 significant figures.

**Ambiguous Zeros**: Can be confusing; use scientific notation to clarify.- Example: 24,000 can be written variously in scientific notation to show different significant digits.

**Exact Numbers**: Have an infinite number of significant figures (e.g., definitions and counting numbers like 12 inches = 1 foot, 14 sheets of paper).

**Multiplication and Division**: The number of significant figures in the result is limited by the measurement with the smallest number of significant figures.- Example: 6.38 × 2.0 = 13 (rounded to 2 significant figures).

**Addition and Subtraction**: The number of decimal places in the result is determined by the measurement with the least number of decimal places.- Example: 6.8 + 11.934 = 18.7 (rounded to the tenths place).

**End of Calculations**: Round only at the end of the calculation.**Weakest Link Principle**: The result of a calculation cannot be more precise than the least precise measurement in the calculation.- Multiplication/Division: Least number of significant figures.
- Addition/Subtraction: Least number of decimal places.