Dimensional Analysis Any valid physical formula must be dimensionally consistent — each term must have the same “dimensions” (You can think in terms of.

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Presentation transcript:

Dimensional Analysis Any valid physical formula must be dimensionally consistent — each term must have the same “dimensions” (You can think in terms of units rather than “dimensions” if you prefer) Examples: distance = velocity × time velocity = acceleration × time energy = mass × (velocity)2

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Clicker Question: How many sig figs does this number have? 0.0037600 A) 3 B) 4 C) 5 D) 6 E) 7

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity Example: What is…

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity Example: What is…

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity Example: What is…

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity Example: What is…

Significant Figures Accuracy of measurements is limited Significant figures: the number of digits in a quantity that are known with certainty Number of significant figures after multiplication or division is the number of significant figures in the least-known quantity For addition or subtraction, line up the decimal points Example: What is…

Scientific Notation Leading or trailing zeroes can make it hard to determine number of significant figures: 2500, 0.000036 Each of these has two significant figures Scientific notation writes these as: a number from 1–10 (the mantissa) multiplied by a power of 10 (the exponent) This makes the number of significant figures much clearer: 2500 = 2.5 × 103 (two sig figs) 2500 = 2.50 × 103 (three sig figs) 2500 = 2.500 × 103 (four sig figs) On your calculator – use the scientific notation key, NOT the [10x] key !!!!

Round-off Error Keep extra digits throughout your calculations – only round off at the end. Two answers that are different only in the least significant digit (and usually only by 1) are probably the result of different rounding.