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Lecture slides for Mr. Mason's Science class.

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- 1. Scientiﬁc Measurement Certainty, Uncertainty and Signiﬁcant Figures
- 2. Certainty and Uncertainty calibrations • Certainty in measurement depends • upon the calibrations and the ability of the user.
- 3. Certainty and Uncertainty Example: Consider a centigram balance whose pointer lies between 32.5 and 32.6. A casual user records the mass 32.5 g while a skillful user records 32.54 g.
- 4. Certainty and Uncertainty 32.54 g The 3,2 and 5 are called certain digits because the were read from the calibrations on the scale. The 4 is said to be uncertain because it is the estimated value between the .5 mark and the .6 mark
- 5. Certainty and Uncertainty RULE In a recorded measurement, the last written digit is assumed to be uncertain.
- 6. Signiﬁcant Figures (”Sig Figs”) Signiﬁcant ﬁgures are deﬁned as all the digits in a measurement that are certain followed by one digit which is an estimate.
- 7. Rules for Counting Signiﬁcant Figures All digits 1-9 inclusive are signiﬁcant. • Example: 12.9g has 3 sig ﬁgs •
- 8. Rules for Counting Signiﬁcant Figures Zeros between two sig ﬁgs are • signiﬁcant Example: 105ml has 3 sig ﬁgs •
- 9. Rules for Counting Signiﬁcant Figures Trailing zeros, after a decimal point, • indicate certainty and are signiﬁcant. Example: 7.00km has 3 sig ﬁgs •
- 10. Rules for Counting Signiﬁcant Figures Zeros that serve only to place the • decimal point are NOT signiﬁcant. Example: 0.001mg has 1 sig ﬁg • 700 mg has 1 sig ﬁg
- 11. Calculating with Signiﬁcant Figures Determine the perimeter of Rectangle D length measured with ruler B 12.0 cm length measured with ruler B 12.0 cm width measured with ruler C 10.52 cm width measured with ruler C 10.52 cm 45.04 cm Answer :
- 12. Calculating with Signiﬁcant Figures Determine the perimeter of Rectangle D length measured with ruler B 12.0 cm length measured with ruler B 12.0 cm width measured with ruler C 10.52 cm width measured with ruler C 10.52 cm 45.04 cm Answer : 45.0 cm
- 13. Rules for Calculating with Signiﬁcant Figures When adding and subtracting, limit and round your answer to the least number of decimal places in any of the addends, minuends or subtrahends.
- 14. Calculating with Signiﬁcant Figures Determine the Area of Rectangle D Recorded width +0.1 12.0 cm x 10.5 cm = 126.0 cm2 recorded values 12.0 cm x 10.4 cm = 124.8 cm2 Recorded width -0.1 12.0 cm x 10.3 cm =123.6 cm2 Answer :
- 15. Calculating with Signiﬁcant Figures Determine the Area of Rectangle D Recorded width +0.1 12.0 cm x 10.5 cm = 126.0 cm2 recorded values 12.0 cm x 10.4 cm = 124.8 cm2 Recorded width -0.1 12.0 cm x 10.3 cm =123.6 cm2 Answer : 125 cm3
- 16. Rules for Calculating with Signiﬁcant Figures When multiplying and dividing, limit and round your answer to the least number of signiﬁcant ﬁgures of any factor, divisor or dividend.
- 17. Precision and Accuracy Precision is indicated by the amount of agreement between two or more measurements that have been made in the same way.
- 18. Precision and Accuracy Student A Student B 17.63g 17.63g 17.64g 17.60g 17.62g 17.66g 17.63g mean 17.63g Even though the averages are the same, student B has a variation of .06 while student A has a variation of .02 g indicating greater precision.
- 19. Precision and Accuracy Accuracy indicates the nearness of a measurement of its “true” value and requires an accurate instrument. An accurate instrument is one that has been calibrated to an accepted standard.

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