1. Significant Figures Calculate: 12.76 x 1.76 = How do we round our answers? –Answer: Significant Figures (Sig Figs) When calculating using measurements, the uncertainty must be reflected in the final answer.

2. Sig Fig Rules Any non-zero digit is significant Zero’s are only significant when: –Between two significant digits 12.01 15505

3. –The last zero after the decimal and after a significant digit 5.350 5.3500 15.00 34.0670.00050 –Zero has a line over the top or a decimal after it 1350 470000. 5000

4. Examples: 5700 12.01.0005050 18000 13450. 5.00 1845 895.045

5. Mass of a Hydrogen atom:.00000000000000000000000067g 2.0g of H 2 is composed of: 602000000000000000000000 molecules Are you sick of writing zeroes yet? There must be a better way... Scientific Notation Review

6. Scientific Notation!! The solution is Exponential or Scientific notation Numbers are written as a product of 2 numbers –a coefficient –a power of 10 The coefficient is a number >1 and <10 Ex. 2.3 x 10 3 = 2.3 x 10 x 10 x 10 = 2300 The exponent represents the number of places the decimal point has been moved from its standard notation point

7. Negative Exponents For numbers that are less than 1, the exponent is NEGATIVE Ex.7.2 x 10 -4 =

8. Sample Problems 1)20000 2)40230000 3)628000 4) 34.1 5).05550 6).099 7) 120.00 8)1.0010 9)2456

9. Accuracy vs. Precision Scientific measurements must be both accurate and precise. Accuracy: How close a measurement comes to the actual dimension or true value of whatever is measured Precision: A instrument is considered precise when it gives the same answer over and over. The measurement is reproducible. Dartboard Analogy:

10. Sig Fig’s in Calculations Multiplication and Division rules: –The measurement with the smallest number of sig figs determines how many are allowed in the final answer 2.3 x 3.76 x 8.275 = ? 6.734 / 2.11 = ? Why? An answer cannot be more precise than the least precise measurement used

11. Significant Figures are only counted in measured numbers. Exact numbers have unlimited sig figs. Example:KE = 1/2mv 2 1 mole = exact number

12. Addition and Subtraction rules: –the number of significant digits allowed depends on the precision of the instruments used Jimmy throws a 2.54 kg rock into a 15000 kg dump truck. What is the mass of the truck? Is is true to say the mass is 15002.54 kg? NO! The mass of the truck is still approximately 15000 kg –Examples: 12.543 + 3.5 = 0.0056 1.2 +19.85