How Reliable are Measurements? Objectives: Define and compare accuracy and precision. Use significant figures and rounding to reflect the certainty of data. Use percent error to describe the accuracy of experimental data.

Accuracy and Precision Accuracy – how close is your answer to the “correct” or “accepted” value? Precision – how close are a series of repeated measurements? (Can you get the same or close answer over and over?)

Accuracy and Precision, cont.

Accuracy and Precision, cont. Density Data Collected By 3 Different Students Student A Student B Student C Trial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3 Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3 Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3 Average 1.51 g/cm3 The actual density was 1.59 g/cm3. 1. Which student was the most accurate? 2. Which student was the most precise?

Percent Error Percent Error = |experimental value- accepted value| X 100 accepted value If the experimental value is 1.54 g/cm3, and the accepted value is 1.59 g/cm3, what is the percent error? Refer to Example Problem on p.38 for answer.

Rules for Significant Figures Non-zero numbers are ALWAYS significant. 72.3 Zeros BETWEEN non-zero numbers are significant. 7023 All FINAL zeros AFTER the decimal point are significant. 72.3000 Zeros that act as place-holders are NOT. (If they disappear when you convert the number to scientific notation, they are not significant.) 7200 = 7.2 x 103 0.0072 = 7.2 x 10-3 Counting numbers and defined constants are ALL significant numbers. 60 s = 1 min

Practice How many significant figures in the following masses? 405,000 kg ***Ended here on Tuesday!!!

Calculations With Significant Figures Addition/Subtraction – Your final answer can only have the same number of numbers to the right of the decimal point as your value with the FEWEST digits to the right of the decimal point. Example: 28.0 + 23.538 + 25.68 = 77.218 Which value has the fewest decimal places? Final answer?

Put It All Together Assignment: Practice Problems (p.39): 31, 32 Practice Problems (p.41): 35, 36 (Let’s look at 36c!!!) Practice Problems (p.42): 37, 38 Section Review (p.42): 39-41

Calculations With Significant Figures, cont. Multiplying/Dividing – Your final answer can only have the same number of significant figures as the measurement with the fewest significant figures. Example: 3.20 x 3.65 x 2.05 = 23.944 Which value has the fewest significant figures? Final answer? What if the first value had been 3.2?