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The Science of PhysicsSection 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

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The Science of PhysicsSection 2 Main Topics Identifying and using significant figures Using scientific notation Converting

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The Science of PhysicsSection 2 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.

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The Science of PhysicsSection 3 Section 2 Measurements in Experiments Chapter 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.

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The Science of PhysicsSection 3 Section 2 Measurements in Experiments Chapter 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.

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The Science of PhysicsSection 3 Chapter 1 Rules for Determining Significant Zeros Section 2 Measurements in Experiments

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The Science of PhysicsSection 2 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.

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The Science of PhysicsSection 3 Chapter 1 Rules for Rounding in Calculations Section 2 Measurements in Experiments

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The Science of PhysicsSection 2 Rounding Round to 3 figures: –30.24 –32.25 –32.65000 –22.49 –54.7511 –54.75 –79.3500

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The Science of PhysicsSection 3 Chapter 1 Rules for Calculating with Significant Figures Section 2 Measurements in Experiments

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The Science of PhysicsSection 2 Calculating with Significant Figures 97.3 + 5.85 123 x 5.35

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The Science of PhysicsSection 2 Identifying and using significant figures Using scientific notation Converting

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The Science of PhysicsSection 3 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 10 3 m) Right is a negative exponent 0.00012 m (1.2 x 10 -3 m)

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The Science of PhysicsSection 3 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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The Science of PhysicsSection 3 SCIENTIFIC NOTATION The very large measurement 310,000,000 m can be rewritten: 3.1 x 10 8 m number 10 multiplied by itself 8 times

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The Science of PhysicsSection 3 SCIENTIFIC NOTATION The very small measurement 0.00000071 can be rewritten: 7.1 x 10 -7 number 1 divided by 10 multiplied by itself 7 times 1 10 7

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The Science of PhysicsSection 3 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 10 8 x 85 Enter the number ‘3’ Press 2 nd 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 10 10

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The Science of PhysicsSection 3 Identifying and using significant figures Using scientific notation Converting

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The Science of PhysicsSection 2 Prefixes

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The Science of PhysicsSection 3 http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/tab/T045196A.gif Prefixes represent different powers of ten

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The Science of PhysicsSection 2 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. 10 3 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

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The Science of PhysicsSection 2 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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The Science of PhysicsSection 3 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) t 2, what dimensions must the 4.9 have in order to be consistent? –Answer: length/time 2 (because y is a length and t is a time) –In SI units, it would be 4.9 m/s 2. Always use and check units for consistency.

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The Science of PhysicsSection 3 How do I interpret the prefixes? 1 meter is 10 0 power 10 meters are 10 1 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 10 3 power or 1000 m (three powers of ten more than 1 meter or three decimal places greater) –giga- is 10 9 power or 1,000,000,000 m (nine powers of ten more than one meter or nine decimal places greater)

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The Science of PhysicsSection 3 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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The Science of PhysicsSection 3 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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The Science of PhysicsSection 3 Meters in a kilometer? 10 3 m = 1 km 1000 m = 1 km Meters in a millimeter? 10 -3 m = 1 mm 0.001 m = 1 mm

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The Science of PhysicsSection 3 Section 2 Measurements in Experiments Chapter 1 Sample Problem A typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms. Given: mass = 2.0 fg Unknown: mass = ? g mass = ? kg

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The Science of PhysicsSection 3 Section 2 Measurements in Experiments Chapter 1 Sample Problem, continued Build 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.

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