Accuracy vs. Precision Measurements need to accurate & precise. Accurate -(correct) the measurement is close to the true value. Precise –(reproducible) several measurements are close in value.

Good Precision Good Accuracy Poor Precision Poor Accuracy Good Precision Poor Accuracy Accuracy vs. Precision

Sources of Error human (mistakes in experiment, measurements, etc.) equipment (faulty or broken equipment, etc.) Calculating Error Accepted Value - true (correct) value - look it up. Experimental Value - measured in lab Error = Accepted value - Experimental value

Example You look up the density of water & it is 1 g/ml You calculate the density in the lab to be 0.8g/ml Error = 1 g/ml - 0.8g/ml = 0.2 g/ml

Percent Error Formula =  Accepted value- calculated value  x 100 Accepted value Example Accepted value for the density of water is 1 g/ml You calculate the density in the lab to be 0.8g/ml % error =  0.2 g/ml  x 100 = 20% error 1 g/ml absolute value of the error makes it a positive number The units cancel out so it is a %

Scientific Notation the product of two numbers: a coefficient & a power of 10. Ex: 3.6 x the coefficient must be greater than 1 but less than 10. there is only one number to the left of decimal. Ex:

Practice: Write the following in scientific notation: =_____________ =______________ 1343= _____________ 0.791= ____________

Scientific Notation on a Calculator GET OUT YOUR CALCULATOR!!! Type in the coefficient (use +/- if needed) EE or EXP (use 2nd or inv. if needed) exponent (use +/- if needed) Example: 3.0 x 10 4 Type in 3.0 push the EE or EXP Type in 4

Multiplying Scientific Notation (practice on your calculator) (3.6 x 10 4 ) x (2.22 x ) What’s happening? Multiply coefficients and ADD exponents. How to do it on a calculator: Type in 3.6 push the EE or EXP button Type in 4 (use +/- if needed) push multiply Type in 2.22 push the EE or EXP button Type in 2 (use +/- if needed) push =

Dividing Scientific Notation How to do it on a calculator: Follow the same steps as above but divide instead of multiply (1.98 x 10 4 ) = (2.34 x ) What’s happening mathmatically? Divide coefficients & SUBTRACT exponents.

Adding/Subtracting: 5.40 x x 10 2 = How to do it on a calculator: Follow the same steps as above but add/subtract instead of multiply. What’s happening? the exponents are made then same then add/subtract coefficients.

Significant Figures Rules: 1)In science we only record significant figures. 2) All digits are significant starting with the first non-zero digit on the left Examples:  3 sig fig  2 sig fig  6 sig fig

Significant Figures Rules: 3) Exception to the rules: If a whole number ends in zero the zeros at the right are not significant. Examples: 15,000  2 sig fig 150  2 sig fig 20,650  4 sig fig 6.0  2 sig fig

Significant Figures ?’s 1) How do you represent 15,000 if all the figures are significant? x ) What if only the 1st 3 places were significant? 1.50 x 10 4 Calculating Significant Figures Multiplying or dividing: the final answer can have no more sig figs than the least reliable measurement. 25 x 25 = 625  should only have 2 sig figs so round off to 630

Calculating Significant Figures Addition and Subtraction: Only keep sig figs when the places match up. 16.5? 8.44?  round off  round off