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SIGNIFICANT DIGITS

SIGNIFICANT DIGITS. Measurement and Calculated Answers. every measurement, taken from a measuring device such as a stopwatch, a balance, or a graduated cylinder has some uncertainty in it. the opposite of uncertainty in a measurement is certainty.

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SIGNIFICANT DIGITS

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  1. SIGNIFICANT DIGITS

  2. Measurement and Calculated Answers • every measurement, taken from a measuring device such as a stopwatch, a balance, or a graduated cylinder has some uncertainty in it • the opposite of uncertainty in a measurement is certainty • the certainty of a measurement is expressed by the number of “certain” or significant digits

  3. a measurement’s certainty is the number of certain digits obtained from the measuring device • rule for counting significant digits is: All digits included in a written measurement are significant except:(i) leading zeros (ii) trailing zeros to the left of the decimal point in measurements larger than one

  4. example #1 For each of the following measurements state the number of significant digits. Measurement # of significant digits 5.2 m two 999 s three 0.125 cm three 450 m two 0.608 g three 3005 m four 0.0035 mL two

  5. certainty rule for multiplying or dividing measurements: When multiplying and/or dividing, the answer has the same number of significant digits as the starting measurement with the fewest number of significant digits. example #2: What is the density of a liquid with a volume of 25 cm3 and a mass of 29.8 g? Express the answer to the correct degree of certainty. D = m/v = 29.8/ 25 = 1.192 = 1.2 g/ cm3

  6. “SIG DIGS” PRACTICE • Complete all questions on p.89 in your course package

  7. Magnification • Concave mirrors can be used to magnify objects • How much larger or smaller an image is compared to the actual object

  8. Magnification • Expressed as a ratio of image height to object height, or image distance to object distance, e.g. OR

  9. Magnification • Use the same units for both heights or both distances in the calculation • No units are required in the answer since the units cancel out • If the image is BIGGER than the object, the magnification will be GREATER THAN 1 • If the image is SMALLER than the object, the magnification will be LESS THAN 1

  10. EXAMPLE PROBLEM • A microscope produces an image that is 5.50 x 10-4 m high from an object that is 2.00 x 10-6 m high. What is the magnification of this microscope?

  11. “G.R.A.S.P” METHOD • G = Given • R = Required • A = Analyze (formula) • S = Substitute (numbers) and Solve • P = Paraphrase (sentence)

  12. SOLUTION • Given: - Object height ho = 2.00 x 10-6 m • Image height hi = 5.50 x 10-4 m • Required: • Magnification, M = ? • Analysis:

  13. SOLUTION • Substitute and Solve: M = 5.50 x 10-4 m = 275 • Paraphrase: - The magnification of the microscope is 275X 2.00 x 10-6 m

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