Cruise around to as many of the Measurement Stations as you can in 5 minutes For each, the answer is on the back Note: Your measurement may vary, but you should have the same # of decimal places recorded and the same +/- as I do Warm-up

How to find the +/- uncertainty of measured and calculated values IB Chemistry Uncertainties

How many candies are in this jar? Do this… Make a guess Compare with 3 others Make a quick bar graph of your 3 guesses and the average Display graph on the blackboard Which group had the highest precision? Precision= ability of a measurement to be consistently reproduced Which had the highest accuracy? Accuracy= a measurements correctness

Significant Figures Since you work hard to be accurate, it’s important that you show off just how careful you were with your measurements. Examples: 76.0cm cm cm 3

Significant Figures Significant Figures are values that have been measured (and deserve respect) 1.98 = 3 sig figsNumbers are significant 2 = 1 sig fig 2.05 = 3 sig figsZeros are sig. if between numbers 2.00 = 3 sig figsZeros are sig. if behind decimal = 1 sig fig … and not at the beginning 2000 = 1 sig fig (but, = 4 sig figs)Zeros at the end are not significant x 10 3 = 4 sig figsEverything is sig. in scientific notation Adding and subtracting- keep the same # of digits after the decimal as the value with the least #s after decimal. Ex: = = 2.7 Multiplying and Dividing- keep the same # of sig figs as the value with the least Ex: x = = Note: Just worry about these at the end and they’re really not too bad.

What is “Uncertainty”? Every time we measure a value, there’s a certain point where we (or the instrument that we’re using) have to estimate or round So, no measurement is absolutely perfect The imperfectness is the uncertainty This can be expressed with a ± value at the end Example: 2.5cm ± 0.5 means that the actual value is 2.0 – cm ± 0.05 means The second value is more precise (note: uncertainties only have 1 significant figure)

Finding Uncertainty- Measured Analog equipment: ± HALF of the increment on the instrument, but you could use your judgment here, with a short justification statement Ex: 76.0cm 3 ± 0.5 (or even 76.0cm 3 ± 0.2 with justification) Ex: 6.55cm 3 ± 0.05 Digital equipment: ± WHOLE last digit measured Ex: 1.25g ± 0.01g Ex: pH= 6.5 ± 0.1

Try some… Measuring mass on a digital balance: 0.34g g Measuring temperature with digital thermometer: 24 o C 19.6 o C Measuring temp with a manual thermometer: 14.5 o C Measuring volume with a burette: 34.5cm 3 ± 0.01 ± ± 1 ± 0.1 ± 0.5

Finding Uncertainty- Calculated I (Propagation of Error) Adding and Subtracting: Add uncertainties of all values used Ex: Volume change = ± 0.05 cm 3 – ± 0.05 cm 3 Could be as small as – = Could be as large as – = So… = ± 0.1 Ex #2: Mass change = 0.8 ± 0.1 g – 0.7 ± 0.1 g = 0.1 ± 0.2 Averaging: Half of the range of values averaged, or the ±, whichever is bigger Ex: average these values: 3.4, 2.6, 3.2 (all ± 0.1) 3.1 ± Uncertainties ALWAYS have only 1 significant figure

Try Some- Addition/Subtraction (45 ± 1)+(23 ± 1) = (0.9 ± 0.1)+(0.8 ± 0.1)–(0.5 ± 0.1) = Average: 9.1 ± 0.1, 9.5 ± 0.1, and 9.2 ± 0.1 = 68 ± ± ± 0.2

Finding Uncertainty- Calculated II Multiplying and Dividing Convert all uncertainties into percents Add the percents Convert the percent back into an absolute uncertainty Ex: Density = (4.5g ± 0.1)/(9cm 3 ± 1) 0.1 is 2.2% of is 11.1% of 9 Density = 0.5g/cm 3 ± 13.3% 13.3% of 0.5 is 0.07 Answer… Density = 0.5 ± 0.07 Don’t forget significant figures at the end

Try Some– Multiplication/Division Rate = (23.9m ± 0.1)/(134sec ± 1) % Water = (0.049g ± 0.001)/(0.092 ± 0.001) 0.1 = 0.42%, 1 = 0.75% Rate = 0.178m/sec ± 1.17% Rate = 0.178m/sec ± = 2.0%, = 1.1% % Water = 53% ± 3.1% of 53 % Water = 53% ± 2

A Quickie Way Usually, the range of your data is much larger than the propagated uncertainty Calculate the final value using your trials, average your trials and then add a ± using ½ of the range to your final answer… This could save you a lot of converting to percents…. blah blah blah along the way Example:

Example– Quickie way 3 values are calculated using the cumbersome % method: ± ± ± 0.03 Average= Uncertainty is half of the range or the uncertainty of the value whichever is larger The range is = 3.04 half of which is 1.52 or 2 with one sig fig 2 is huge compared to the uncertainties of the values, so why did you bother with all that mess? Just skip it! Answer = ± 2