The Science of Physics Section 2

Unit Outline--Topics

• What is Physics?• Branches of Science• Science Terms• Scientific models• Measuring and Units• Powers of Ten and conversions• Graphing• Experimental Design• Science vs. Technology • Analyzing in Physics

The Science of Physics Section 2

Main Topics

• Identifying and using significant figures• Using scientific notation• Converting

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Significant Figures

• Significant figures are the method used to indicate the precision of your measurements.

• Significant figures are those digits that are known with certainty plus the first digit that is uncertain.– If you know the distance from your home to school is

between 12.0 and 13.0 miles, you might say the distance is 12.5 miles.

• The first two digits (1 and 2) are certain and the last digit (5) is uncertain.

The Science of Physics Section 3Section 2 Measurements in ExperimentsChapter 1

Significant Figures

• It is important to record the precision of your measurements so that other people can understand and interpret your results.

• A common convention used in science to indicate precision is known as significant figures.

• Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

The Science of Physics Section 3Section 2 Measurements in ExperimentsChapter 1

Significant Figures, continued

Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.

The Science of Physics Section 3Chapter 1

Rules for Determining Significant Zeros

Section 2 Measurements in Experiments

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Counting Significant Figures

• Examples– 50.3 m– 3.0025 s– 0.892 kg– 0.0008 ms– 57.00 g– 2.000 000 kg– 1000 m– 20 m

• Scientific notation simplifies counting significant figures.

The Science of Physics Section 3Chapter 1

Rules for Rounding in Calculations

Section 2 Measurements in Experiments

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Rounding

• Round to 3 figures:

– 30.24– 32.25– 32.65000– 22.49– 54.7511– 54.75– 79.3500

The Science of Physics Section 3Chapter 1

Rules for Calculating with Significant Figures

Section 2 Measurements in Experiments

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Calculating with Significant Figures

• 97.3 + 5.85

• 123 x 5.35

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• Identifying and using significant figures• Using scientific notation• Converting

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SCIENTIFIC NOTATION

• Used by scientists and engineers to express very large and very small numbers.

• Changes by powers of ten

• Count decimal places either to the right or left

• Left is a positive exponent

1200 m (1.2 x 103 m)• Right is a negative

exponent0.00012 m (1.2 x 10-3

m)

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What is a power of ten?

• A power of ten represents a decimal place.

• One power of ten can mean ten times less or ten times greater.

Examples

• 10 m and 1 m differ by one decimal place or one power of ten.

• 0.001 m and 0.00001 m differ by two decimal places or two powers of ten.

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SCIENTIFIC NOTATION

• The very large measurement 310,000,000 m can be rewritten:

3.1 x 108 m

number

10 multiplied by itself 8 times

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SCIENTIFIC NOTATION

• The very small measurement 0.00000071 can be rewritten:

7.1 x 10-7

number1 divided by 10 multiplied by itself 7 times

1

107

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SCIENTIFIC NOTATION AND YOUR CALCULATOR• It is possible to compute using numbers written in

scientific notation.• Here’s how it’s done: For 3 x 108 x 85• Enter the number ‘3’• Press 2nd and then the ‘EE’ key. Some calculators (Casio) use

the ‘EXP’ key • Enter ‘8’ for exponent (press the -/+ key if exponent is negative)• Press multiplication key • Enter ‘85’• Press = to solve the problem • Answer is 2.55 x 1010

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• Identifying and using significant figures• Using scientific notation• Converting

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Prefixes

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http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/tab/T045196A.gif

Prefixes represent different powers of ten

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Converting Units

• Build a conversion factor from the previous table. Set it up so that units cancel properly.

• Example - Convert 2.5 kg into g.– Build the conversion factor:

– This conversion factor is equivalent to 1.• 103 g is equal to 1 kg

– Multiply by the conversion factor. The units of kg cancel and the answer is 2500 g.

• Try converting – .025 g into mg– .22 km into cm

310 g

1 kg

3 10 g2.5 kg 2500 g

1 kg

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Classroom Practice Problem

• If a woman has a mass of 60 000 000 mg, what is her mass in grams and in kilograms?– Answer: 60 000 g or 60 kg

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Dimensional Analysis

• Dimensions can be treated as algebraic quantities.– They must be the same on each side of the equality.

• Using the equation y = (4.9)t2 , what dimensions must the 4.9 have in order to be consistent?– Answer: length/time2 (because y is a length and t is a

time)– In SI units, it would be 4.9 m/s2 .

• Always use and check units for consistency.

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How do I interpret the prefixes?

• 1 meter is 100 power• 10 meters are 101 power

– milli- is 10-3 power or 0.001 m (three powers of ten less than 1 meter or three decimal places less)

– kilo- is 103 power or 1000 m (three powers of ten more than 1 meter or three decimal places greater)

– giga- is 109 power or 1,000,000,000 m (nine powers of ten more than one meter or nine decimal places greater)

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Why Convert?• To compare the results

from measurements using different units, one unit must be converted into the other unit.

• Two basic types– System conversions

• English to metric• example: inches to

centimeters

– Power of ten conversions • Change in prefix reflects

powers of ten • example: meters to

centimeters

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How do you convert?

• Use the factor-label method (also called dimensional analysis)

• 1. decide what must be converted

• 2. select conversion factor

• 3. set up factoring equation

• 4. perform math and solve

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Meters in a kilometer? 103 m = 1 km

1000 m = 1 km

Meters in a millimeter? 10-3 m = 1 mm

0.001 m = 1 mm

The Science of Physics Section 3Section 2 Measurements in ExperimentsChapter 1

Sample ProblemA typical bacterium has a mass of about 2.0 fg.

Expressthis measurement in terms of grams and

kilograms.Given: mass = 2.0 fg

Unknown: mass = ? g mass = ? kg

The Science of Physics Section 3Section 2 Measurements in ExperimentsChapter 1

Sample Problem, continuedBuild conversion factors from the relationships

given in Table 3 of the textbook. Two possibilities are:

Only the first one will cancel the units of femtograms to give units of grams.

–15

–15

1 10 g 1 fg and

1 fg 1 10 g

–15–151 10 g

(2.0 fg) = 2.0 10 g1 fg