1 § 02-03 Using Scientific Measurements A. Accuracy and Precision

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§ 02-03 Using Scientific Measurements

A. Accuracy and Precision

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•Accuracy:= closeness of measurements to the correct or accepted value of the quantity measured.

•Precision:= closeness of a set of measurements of the same quantity made in the same way.


3

•Precision:= closeness of a set of measurements of the same quantity made in the same way.


4HIGH LOWAccuracy: Precision:

5Accuracy: Precision:LOW HIGH

6Accuracy: Precision:LOW LOW

7Accuracy: Precision:HIGH HIGH

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Age (yrs) of Students in CHEM 320

Class A Class B Class C

17.0 25.0 4.5

15.4 10.2 4.3

15.8 22.1 4.2

16.2 12.1 4.3

15.9 10.3 5.3

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§ 02-03 Using Scientific Measurements

B. Percent Error

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•To give meaning to experimental data, it is often helpful to compare them with the ‘correct’ or accepted values by calculating the PERCENT ERROR.

B. Percent Error

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Calculate by: (p. 45)

B. Percent Error

accepted

alexperimentaccepted

Value

ValueValueErrorPercent

100% x Value


accepted


12

Example:A student measures the mass of an object to be 24.21 g and its volume to be 11.32 mL. The known density of the substance is 2.00 g/mL. What is percent error of the student’s measurement?

accepted


Value


13

Example:A student measures the mass of an object to be 24.21 g and its volume to be 11.32 mL. The known density of the substance is 2.00 g/mL. What is percent error of the student’s measurement?

accepted


Value


14

density = 24.21 g and its volume to be 11.32 mL.

accepted


Value


g/mL 2.1432.11

21.24

mL

g

g/mL 2.1432.11

21.24:density lexpt'

mL

g

%100/00.2

2.14g/mLg/mL00.2:error % x

mLg

= -7 %

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There is always some error in measurement - even w/ the best technical skill and instruments. General rule of thumb: report to most digits of instrument (and if between, add 1/2 of a unit - e.g., see p. 46 of book)

C. Error in Measurement

accepted


Value


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The length of the nail is definitely between 6.3 cm and 6.4 cm. Because it is about half-way between, it should be read as 6.35 cm, with the understanding that the hundredths place is somewhat uncertain.

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•In science, the certainty of the data is very important. This is inherent in the number of displayed SIGNFICANT FIGURES.

D. Significant Figures

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•In a measurement, the digits known with certainty plus one final digit (which may be known with certainty or estimated) are the significant figures.


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•Significant figures don’t necessarily mean certain, they mean scientifically significant.


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•As a chemistry student, you will need to use and recognize figures when you work with measured quantities and report your results, or evaluate others’.

•There are definite rules of significant figures... (q.v. Table 2-5 - know by usage)


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•As a chemistry student, you will need to use and recognize figures when you work with measured quantities and report your results, or evaluate others’.

•There are definite rules of significant figures... (q.v. Table 2-5 - know by usage)

22

How many significant figures are there in each of the following

measurements?

• 40.5

• 87 009

• 0.01

• 5 280

• 100.01

• sig. fig. = 3(rule 1)

• = 5

(rule 1)

• = 1

(rule 2)

• = 3

(rule 2)

• = 5

(rule 3)

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• 2 000 may contain one or four significant figures (depending on how many zeros are place holders). FOR MEASUREMENTS IN THIS BOOK, ASSUME THAT 2 000 HAS ONE SIGNFICANT FIGURE. TO EMPHASIZE THAT IT HAS FOUR S.F., WRITE: 2 000. (N.B. decimal point). {2 000.0 has 5 s.f.}

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•Read book - if you have any questions, ask Dr. Fisher. But this material should have been covered many times in previous classes.

E. Rounding

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•For multiplication and division, the number of significant figures in the answer can have NO MORE than the fewest number of significant figures in any of the measurements... (e.g...

F. Multiplication & Division of Significant Figures

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/mL579024844g4999123331000.0203.861,6

43.3

mL

g

g/mL000500.0

The fewest significant figures in the measurements is three (3.43 g) - so that’s the what that the answer will have.

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1 § 02-03 Using Scientific Measurements A. Accuracy and Precision