Calculations Notes

Multiplication and Division Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate) Ex 1: 4.63 m x 7.5 mEx. 2: m 2 / 2.1 m 35 m m 3sf 2sf m 2 4sf2sf m

Addition and Subtraction Align the decimal points and carry out the calculation. First column from the left with an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP) Ex 1: g g g Ex. 2: m m GAP 11.3 g GAP 4.39 m

Scientific Notation and Multiplication and Division Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F. Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F. Ex 1: (1.00 x 10 3 m)(3.2 x 10 2 m)Ex. 2: (3.00 x 10 4 g)/(1.0 x 10 2 cm 3 ) 3.2 x 10 5 m x 10 2 g/cm 3

Scientific Notation and Addition and Subtraction must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent Ex 1: 3.0 x m x m x m +.10 x m GAP 3.1 x m

Element Buddies ADD PRACTICE

Problem Solving and Dimensional Analysis Conversion factor – ratio of two parts of the statement that relates the two units Equivalence Statement – true statement in fraction form Dimensional Analysis – when used properly all units will cancel out except the desired unit 2.54 cm = 1 inch100 cm = 1 m 2.54 cm 1 inch 2.54 cm 100 cm 1 m 100 cm oror x ______________ Desired UNIT Wanted UNIT # # x ________________ Wanted UNIT # # Given UNIT Given with UNITS =

Ex. 1: 250 m = ___________ km Ex. 2: 3.54 g = ___________ mg Ex. 3: kg = __________ mg x ___________ km m 250 m =.25 km x ___________ mg g 3.54 g = 3540 mg x __________ mg g x ________ g kg kg = mg

Determining Error ___________________value - correct value based on reliable references ___________________value - value measured in the lab Error = experimental value – accepted value (Note: error can be positive or negative) You will take the ___________ value of this when you calculate percent error. accepted experimental absolute

Determining Percent (%) Error Percent error = absolute value of error divided by accepted value and multiplied by 100% % error = experimental value – accepted value x 100% accepted value Example: You take three temperature readings of a beaker of boiling water and record: 91.3 o C, 90.9 o C, and 91.1 o C. Evaluate accuracy, precision, and error. Accurate? No, water boils at 100 o C Precise? Yes, values are close to each other 1.Find average experimental data 2.Use formula Error (91.3 o C o C o C)/3 = 91.1 o C % error = (91.1 o C – 100 o C) x 100% 100 o C = 8.90 %