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MeasurementMeasurement

DataDataMeasurements and observations.

ResultsResultsData obtained from an experiment.

UnitsUnitsAll measurements must have units.

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Measurements in ChemistryMeasurements in Chemistry

Metric Units Metric Units

Mass g, mg, kgLength m, cm, mm, µsnitchVolume cm3, L, mL

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Common Metric PrefixesCommon Metric Prefixes

.

Prefix Symbol Meaning Examplegiga- G 109 4 GBmega- M 106 6 MBkilo- k 103 2 kmdeci- d 10-1 2 dmcenti- c 10-2 2 cmmilli- m 10-3 2 mmmicro- µ 10-6 2 µm

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Significant FiguresSignificant Figures

Significant figures are the digits in a measurement that are known for sure

plus one estimated digit. The right most digit is always estimated.

612 mL 207 K 0.047 m 3.60 L 10 pens none

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Determining Significant FiguresDetermining Significant Figures

If a measurement is written with an explicit (visible) decimal point, then start at the left most digit.

Move to the right until you find the first non-zero digit.

Count that digit and every digit to the right end of the value or 0. Stop counting at the 0.

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Determining Significant FiguresDetermining Significant Figures

If a measurement is written with an implicit (invisible) decimal point, then start at the right most digit.

Move to the left until you find the first non-zero digit.

Count that digit and every digit to the right end of the value or 0. Stop counting at

the 0.

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Sig FigsSig Figs

. Measurement # of Sig Figs75.456 g 5690 004 km 687 000 000 km 287 000 000 km 60.0007060 kg 40.00033 mg 20.534 L 31.00033 g 6

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Rounding Off CalculationsRounding Off Calculations

If the digit immediately to the right of the last

significant digit you want to keep is:

1) > 5, the last significant digit should be increased by 1, i.e.

42.68 g rounded to 3 sig figs: 42.7 g

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2) < 5, the last significant digit should remain

the same, i.e.

17.32 m rounded to 3 sig figs: 17.3 m

3) 5, followed by nonzero digits, the last significant digit should be increased by 1, i.e.

2.7851 cm rounded to 3 sig figs: 2.79 cm

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4) 5, not followed by nonzero digits, and preceded by an odd digit, then the last significant digit should be increased by

1, i.e.

4.635 kg rounded to 3 sig figs: 4.64 kg

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5) 5, not followed by nonzero digits, and preceded by an even digit, then the last significant digit should remain the same, i.e.

78.65 mL rounded to 3 sig figs: 78.6 mL

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Adding With Significant FiguresAdding With Significant Figures

The sum or difference of measurements must

contain as many decimal places as there are

in the measurement containing the leastnumber of decimal places.

38.102 cm + 18.9984 cm = 57.100 cm3 dp’s 4

dp’s3

dp’s

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Subtracting With Significant Subtracting With Significant FiguresFigures

55.320 g - 6 g = 49 g

3 dp’s 0 dp’s

0 dp’s

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Multiplying With Sig Figs Multiplying With Sig Figs

The product or quotient must contain thesame number of significant figures as themeasurement with the least number ofsignificant figures.

34.2051 mm × 3.22 mm = 110. mm2 = 110 m2

6 sf’s 3 sf’s 3 sf’s 3 sf’s

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Dividing With Sig FigsDividing With Sig Figs

57.90 g/7.41 mL = 7.81 g/mL

4 sf’s 3 sf’s 3 sf’s

Units do not cancel, therefore g/mL!

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Dimension Analysis – Factor LabelDimension Analysis – Factor Label

1) 14.5 km = ? m

14.5 km x

103 m 1 km

= 1.45 x 104 m

2) 3.54 g = ? mg

3.54 g x

103 mg 1 g

= 3.54 x 103 mg

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Dimension Analysis – Factor LabelDimension Analysis – Factor Label

3) 125 cm = ? m

125 cm x

1m102 cm

= 1.25 m

4) 0.5420 kg = ? mg

0.5420 kg x 103 g 1 kg

x 103 mg 1 g

=5.420 x 105 mg

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Density ProblemsDensity Problems

A sample of oil has a density of 0.916 g/mL.

(a)What is the mass of 225 mL of the oil?

(b)What volume is occupied by 45.0 g of the oil?

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(a)D = 0.916 g/mL V = 225 mL

D =

m = D × V = 0.916 mLg×225 mL = 206 g

(b) m = 45.0 g

V = = 45.0 g0.916

mLg=

49.1 mL

Vm

Dm

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Density ProblemDensity Problem

A block of copper 6.00 cm long, 3.50 cmwide, and 4.00 cm thick has a mass of 1802

g.What is the density of the copper?

l = 6.00 cmw = 3.50 cmh = 4.00 cmm = 1802 g

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.

D =

V = l × w × h

V = 6.00 cm × 3.50 cm × 4.00 cm = 84.0 cm3

D = 1802 g84.0 cm3

= 21.4 g/ cm3

Vm

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Accuracy and PrecisionAccuracy and Precision

Accuracy measures how close yourmeasured value agrees with the acceptedvalue.

Precision measures the reproducibility ofyour measurements.

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Good Accuracy and Good Good Accuracy and Good PrecisionPrecision

.

××× ××

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Poor Accuracy and Good PrecisionPoor Accuracy and Good Precision

.

×××××

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Poor Accuracy and Poor PrecisionPoor Accuracy and Poor Precision

.

×

×

×

×

×

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Percent ErrorPercent Error

% error = AAO × 100%

O is the observed value which is determined by experiment.

A is the accepted value or the true value.

Only the magnitude (size) matters, therefore you ignore plus and minus signs.

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Percent ErrorPercent Error

The accepted value for the boiling point ofmethyl alcohol is 65.0°C. In the lab, youmeasured the boiling point to be 64.0°C.What is your percent error?

O = 64.0°C A = 65.0°C

%error = AAO ×100%

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Percent ErrorPercent Error

.

%error = 64.0°C – 65.0°C65.0°C

×100%

%error = 1.54%