ScientificMeasurement

Chapter 3

Steps in the Scientific Method1. Observations

- quantitative- qualitative

2. Formulating Hypotheses- possible explanation for the observation

3. Performing Experiments- gathering new information to decide whether the hypothesis is valid

Part 1 - Part 1 - number number

Part 2 - Part 2 - scale (unit)scale (unit)

Examples: Examples:

2020 grams grams 6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds

Measurement - quantitative Measurement - quantitative observation observation consisting of 2 partsconsisting of 2 parts

Nature of MeasurementNature of Measurement

(le Système International, SI)(le Système International, SI)

Physical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance mole mol

Luminous Intensity candela cd

The Fundamental SI UnitsThe Fundamental SI Units

SI Prefixes Common to Chemistry

Prefix Unit Abbr. Exponent

Mega M 106

Kilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9

Pico p 10-12

Uncertainty in Measurement

A digit that must be A digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always has always has some degree of uncertainty.some degree of uncertainty.

Measurements are performed with instruments No instrument can read to an infinite number of decimal places

AccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue (known) (known) value.value.

PrecisionPrecision refers to the degree of agreement refers to the degree of agreement among several measurements made in the among several measurements made in the same manner. (aka – reproducibility)same manner. (aka – reproducibility)

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Precision and Accuracy

Rules for Counting Significant Figures

1. If the number contains a decimal, count from right to left until only zeros or no digits remain.

Examples: 20.05 grams 4 sig figs 7.2000 meters 5 sig figs 0.0017 grams 2 sig figs

2. If the number does not contain a decimal, count from left to right until only zeros or no digits remain.

Examples: 255 meters 3 sig figs 1,000 kilograms 1 sig fig

3. Exact numbers have an infinite number of significant figures.

1 inch = 2.54 cm, exactly

How many significant figures in each of the following?

1.0070 m

5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Sig Fig Practice #1Sig Fig Practice #1

Rules for Significnt Figures in Mathematical Operations

• Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the least precise places in the least precise measurement. measurement.

6.8 + 11.934 = 6.8 + 11.934 =

18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))

Sig Fig Practice #2Sig Fig Practice #2

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Rules for Significant Figures in Mathematical Operations

• Multiplication and DivisionMultiplication and Division:: # sig # sig figs in the result equals the number figs in the result equals the number in the least precise measurement in the least precise measurement used in the calculation. used in the calculation.

6.38 x 2.0 = 6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #3Sig Fig Practice #3

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Converting Celsius to KelvinConverting Celsius to Kelvin

Kelvin = C + 273 °C = Kelvin - 273

Dimensional Analysis- aka: factor label

unit cancellation fence-post

- provides a systematic way of solving numerical problems

Set-up: Given Desired Units___ 1 Units to Eliminate

Dimensional Analysis Examples115 lbs = ______ g

115 lbs 453.6 g 5.22 x 104 g 1 1 lb

Useful Conversions1 mi = 1.6093 km

1 lb = 453.59 g

1 in = 2.54 cm

0F = (9/5) 0C + 32

1 L = 1.0567 qt

1 mL = 1cm

1 kg = 2.2046 lb

0C = (5/9)( 0F – 32 )

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