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UNIT II.5 Significant Figures

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II.5 SIGNIFICANT FIGURES Measuring vs. Counting: Imagine we are picking apples and we count the apples as we go. We can count exactly how many we pick (ex: 30 apples). If we wanted to measure the mass of the apples, it could be done but we cannot measure the EXACT mass of the apples. There is always some ___________________ associated with measurements.

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II.5 SIGNIFICANT FIGURES There are 2 things we need to learn: 1. 2.

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II.5 SIGNIFICANT FIGURES 1. SIGNIFICANT FIGURES A. Definition A significant figure (sig fig) is Ex:

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II.5 SIGNIFICANT FIGURES All non-zero digits are significant. Ex. All zero digits between non-zero digits are significant. Ex.

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II.5 SIGNIFICANT FIGURES Leading zeroes are NOT SIGNIFICANT. Ex:

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II.5 SIGNIFICANT FIGURES Trailing zeroes are ONLY SIGNIFICANT WHEN A DECIMAL POINT IS PRESENT. Ex: QUESTION: p. 37 #55

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II.5 SIGNIFICANT FIGURES B. Accuracy and Precision An ACCURATE measurement = A PRECISE measurement =

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II.5 SIGNIFICANT FIGURES *Note: we calibrate instruments (especially balances) to ensure accuracy. Calibration involves measuring the mass of a known object and adjusting the balance until we obtain the desired reading. The balance has then been calibrated! Example: P 29 #43

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II.5 SIGNIFICANT FIGURES Assume you have a balance which gives very precise measurements. What might be true about the balance that its readings would be precise but not accurate? QUESTIONS: p. 29 #44, 45

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II.5 SIGNIFICANT FIGURES C. Measuring an object or substance…. The NUMBER of significant figures = Examples: * If you are given a measurement without any additional info, assume that the LAST DIGIT is _______________________. Ex: 45. 7

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II.5 SIGNIFICANT FIGURES D. Defined Numbers and Counting Numbers Examples: QUESTIONS: p. 29 #46, 47

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II.5 SIGNIFICANT FIGURES 2. HOW TO READ A SCALE Terms:

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II.5 SIGNFICANT FIGURES Example (a) on p. 30: 1 st 2 digits are 6.2 1 st 2 digits are 6.3

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II.5 SIGNIFICANT FIGURES #1: Find the DIFFERENCE between each numbered division: #2: Find the value of the unnumbered division: *Value at (i) *Value at (ii) #3: Estimate the uncertain digit: *Value at (i) *Value at (ii)

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II.5 SIGNIFICANT FIGURES *NOTE: if the pointer appears to be exactly on one of the marking: Example: QUESTION: p. 32 #48

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II.5 SIGNIFICANT FIGURES 3. EXPERIMENTAL UNCERTAINTY Definition: Experimental uncertainty =

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II.5 SIGNIFICANT FIGURES Ex: 39.1 0.1 C Means that the actual value lies in the range of *The measurement reported is the _______________________ of the range (midpoint is the average of the endpoints).

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II.5 SIGNIFICANT FIGURES 4. MULTIPLYING & DIVIDING NUMBERS Ex:

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II.5 SIGNIFICANT FIGURES Notes *Sometimes you will have to put your number in scientific notation to have the correct # of sig figs: Ex:

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II.5 SIGNIFICANT FIGURES **Exponential parts of the number do NOT contribute to the # of sig figs: Ex: 3.2 x 10 3 *** When performing calculations, dont ROUND until the end (final answer). QUESTION: p. 39 #56 (odd)

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II.5 SIGNIFICANT FIGURES 4. ADDING & SUBTRACTING NUMBERS Ex: 11.467 cm + 12.31 cm *Adding numbers in scientific notation: Ex:

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II.5 SIGNIFICANT FIGURES **Reminder: QUESTIONS: p. 40 #57 and 58 (odd)

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ASSIGNMENT

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Measurements and Their Uncertainty 3.1

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