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Measured & counted numbers • When you use a measuring tool to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers. Counted numbers Obtained when you count objects • 2 soccer balls • 1 watch • 4 pizzas Obtained from a defined relationship • 1 foot = 12 inches • 1 meters = 100 cm Not obtained with measuring tools Measurements: Accurate or Precise? Creating definitions and clarifying terms Precision • Precision is the ability to _______________and come up with the same value every time. • It is an indication of __________a series of measurements are to each other. • In general, the more decimal places you have, the more precise your measurement is. Precision • The idea of precision is very closely aligned with the idea of significant figures. • A large number of significant figures suggests a high degree of precision. • In our next class we will learn all about sig figs. Now, relax Which is the most precise balance? Accuracy • An indication of how ________________________ (often theoretical) The closer you are to the real, accepted value, the more accurate you are. Accurate or Precise? Case 1 • In the diagram, what can we say about the group of arrows in terms of accuracy: precision: Accurate or Precise? Case 1 • In the diagram, what can we say about the group of arrows in terms of accuracy: low (as a group) precision: low Accurate or Precise? Case 2 • In the diagram, what can we say about the group of arrows in terms of accuracy: precision: Accurate or Precise? Case 2 • In the diagram, what can we say about the group of arrows in terms of accuracy: low precision: high Accurate or Precise? Case 3 • In the diagram, what can we say about the group of arrows in terms of accuracy: precision: Accurate or Precise? Case 3 • In the diagram, what can we say about the group of arrows in terms of accuracy: high precision: high Can we ever be 100% certain?? Nope! This is what we call ‘uncertainty’ in measurements. Experimental uncertainty • It is the estimated amount by which a measurement might be in error • Usually expressed as +/• The smaller the uncertainty, the more the precision… Experimental uncertainty Assume you measured a temperature to be 37.5 C° What would the uncertainty be? Uncertainty is always in the last digit! What does this mean? Experimental uncertainty This means, the actual degree is somewhere between How to read a measurement scale Taking measurements Example b) page 31 Volume readings Graduated cylinder readings Time to practice! Hebden page29 #44 page32 #48(A,C,E) page34 #50(A,D,G) page35 #51(A,C) and #52(A,B) I am here to help Measurements • Why do we care?????? • Measured quantities have uncertainties in them. It is impossible to find the EXACT value…so what do we use? Significant figures • They are measured or meaningful digits. How do we know if a number is a ‘sig fig’ or not? • Let us proceed, shall we? Two major cases to know #1: When there are no decimal points #2: When there are decimal points #1: when there are no decimal points • Count every single number you see as a significant figure, EXCEPT for ZERO. • BUT…..Zeroes in between two non-zero digits are significant. All other zeroes are insignificant. #1: when there are no decimal points • How many sig figs do the following numbers have?? 345, 5557, 300, 4120, 4005, 40050 #2: when there are decimal points • Start from the left side of the number, ignore all the zero's on the left side of the decimal points ( aka leading zero's). Only start counting at the first non zero digit. Once you start counting, continue until you run out of digits. #2: when there are decimal points • Example: how many sig figs do the following numbers have? 32.670, 0.0001, 0.034780, 44.4, 00.9090 Significant figures “sig figs” 0.520 0.0025 500 0.02300 120035 500. 2.0 x 105 3 2 1 4 6 3 2 do not expand Significant figures 2.5002 0.00650 5001 0.0200300 0.02010 200 200. 2.0 x 102 2. x 102 “sig figs” 5 3 4 6 4 1 3 2 1 Adding and Subtraction with Significant Figures When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations. 1. 21.036 + 22.1 Adding and Subtraction with Significant Figures When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations 3. 301.2256 - 0.36 Adding and Subtraction with Significant Figures 4. + 8.053 x 104 2.3 x 104 Adding and Subtraction with Significant Figures 5. 2.463 x 105 + 5.006 x 102 Adding and Subtraction with Significant Figures 6. 5.331 x 10-4 - 2.126 x 10-5 When changing exponents, remember…..if you change the lower exponent to the higher exponent. You are making the exponent larger so make the number smaller. It is a trade ! HOMEWORK • PAGE 40 #57 (A,B,C,E,F,I,J)