Significant Figures Calculate: 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.

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

–The last zero after the decimal and after a significant digit –Zero has a line over the top or a decimal after it

Examples:

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

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

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

Sample Problems 1) ) ) ) ) ).099 7) ) )2456

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:

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 = ? / 2.11 = ? Why? An answer cannot be more precise than the least precise measurement used

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

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 kg dump truck. What is the mass of the truck? Is is true to say the mass is kg? NO! The mass of the truck is still approximately kg –Examples: =