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# Sci Measure

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Lecture slides for Mr. Mason's Science class.

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### Sci Measure

1. 1. Scientiﬁc Measurement Certainty, Uncertainty and Signiﬁcant Figures
2. 2. Certainty and Uncertainty calibrations • Certainty in measurement depends • upon the calibrations and the ability of the user.
3. 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. 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. 5. Certainty and Uncertainty RULE In a recorded measurement, the last written digit is assumed to be uncertain.
6. 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. 7. Rules for Counting Signiﬁcant Figures All digits 1-9 inclusive are signiﬁcant. • Example: 12.9g has 3 sig ﬁgs •
8. 8. Rules for Counting Signiﬁcant Figures Zeros between two sig ﬁgs are • signiﬁcant Example: 105ml has 3 sig ﬁgs •
9. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.