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CHAPTER 2 Measurements and Calculations

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Scientific Method System Specific portion of matter that has been selected for study Scientific Method Logical approach to solve a problem

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Scientific Method Steps Observing and collecting data Use of senses Quantitative data – numerical Qualitative data - descriptive Generalization – statements about what is observed Organizing – Graphs, tables, statistics Hypothesis – testable statement Law – statement that DESCRIBES facts

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Scientific Method Steps Theorizing Statement that EXPLAINS facts Can never be proven!! Testing Experimentation

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Units of Measurement Unit of Measurement A physical quantity of a defined size lb, in, ft, g, cm, km SI International System of Units (metric system) Adopted in 1960, originated in France

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SI SI base units – standard of measure – Have a defined size Length – meter (m) Mass – kilogram (kg) Time – second (s) Temperature – Kelvin (K)

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SI Prefixes PrefixSymbolExampleExponential Factor Factor TeraTTerameter10 12 1000000000000 GigaGGigameter10 9 1000000000 MegaMMegameter10 6 1000000 KiloK or kKilometer10 3 1000 HectoHHectometer10 2 100 DecaDDecameter10 1 10 ---- meter10 0 ---- DecidDecimeter10 -1 0.1 CenticCentimeter10 -2 0.01 MillimMillimeter10 -3 0.001 MicroµMicrometer10 -6 0.000001 NanonNanometer10 -9 0.000000001 PicopPicometer10 -12 0.000000000001 Know the ones in BOLD above!!!

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SI Prefixes Number Line – MEMORIZE!! K H D d c m _ _ µ With meters: Examples:

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Derived SI Units Derived Unit – obtained from combining base units Area L * w m 2 Volume L * w * h m 3 Speed Length/time m/s Density Mass/volume g/mL or g/cm 3

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Conversion Factors and Factor-Label Method Factor-Label Method – problem solving method using algebra Conversion Factors = 1 Examples:

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Using Scientific Measurements Accuracy Closeness of a measurement to the true or accepted value Precision Agreement among the values Percent Error Experimental value – Accepted Value x 100% Accepted Value http://honolulu.hawaii.edu/distance/sci122/SciLab/L5/accprec.html

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Measuring Always estimate one more place than the measuring device

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Significant Figures Sig Figs – gives the amount of detail in a measurement How many sig figs in a number? Table 2-5 page 47

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Sig Figs Rules All non-zero numbers ARE significant 3.456 = 4 SF Sandwich zeros ARE significant 306 = 3 SF Leading zeros ARE NOT significant.000239 = 3 SF Trailing zeros: If there IS a DECIMAL POINT WRITTEN the numbers ARE significant Scientific Notation Look at the Number portion before the x10 only 2.31 x 10 3 = 3 SF 3.0 x 10 3 = 2 SF

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Significant Figures Using Sig Figs in Math Operations Multiply/Divide Answer must have number of sig figs as least precise number 2.3 (2 SF) x 5.67 (3 SF) = 13 (2 SF) 16.00 (4 SF) / 8.0 (2 SF) = 2.0 (2 SF) Add/Subtract Answer must have number of “columns” as least precise number 1.03 (hundredths) + 3 (ones) 4

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Significant Figures Rounding off a number – Table 2-6 page 48 Rules – look at number to the right of the last sig fig you want to retain Example Greater than OR EQUAL TO 5, increase the last digit by 1 56.87 g … 56.9 g Less than 5, do not change last digit12.02 L … 12.0 L 5, followed by nonzero digit(s), increase last digit by 1 3.7851 …3.79 5, not followed by nonzero digit and preceded by odd digit(s) increase last digit by 1 2.835 s … 2.84 s 5, not followed by nonzero digit(s) and the preceding sig fig is even, do not change last digit 2.65 mL … 2.6 mL

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Significant Figures Exact numbers -

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Scientific Notation Used to represent very big or very small numbers Generic form: M x 10 N M must be greater than 1 and less than 10 If positive (+) N value = a “big” number If negative (–) N value = a “small” number

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Scientific Notation 4.21 x 10 2 4.21 = number part in standard form (one digit to left of decimal point) 10 2 = tells where decimal is 2 = exponent

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Scientific Notation Converting TO Scientific Notation Move decimal to left = positive exponent Move decimal to right = negative exponent Examples:

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Scientific Notation Calculator Type the “M” Hit the EE or EXP button Type the “N”

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Scientific Notation Math and scientific notation Add/Subtract Exponents MUST be the same!! Add M values and exponent stays the same Multiply Multiply M values and add exponents Divide Divide M values and subtract exponents

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Heat and Temperature Temperature Measure of the AVERAGE kinetic energy of the particles in a sample How hot or cold something is Heat SUM TOTAL of the kinetic energy of the particles in a sample More particles = more heat

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Heat and Temperature Thermometer Device used to measure temperature Hg or alcohol Liquid EXPANDS or CONTRACTS Temp scales °C – Celsius, 0°C, 100°C °F – Fahrenheit, 32°F, 212°F

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How a thermometer works: If liquid is warmer than the thermometer: 1. Heat enters the thermometer 2. Particles of the thermometer liquid move faster 3. Liquid in the thermometer expands 4. Liquid moves up the tube

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Heat and Temperature Kelvin Freezing point of water – 273 K Boiling point of water – 373 K K = °C + 273.15 – memorize!! °C = K – 273.15 Examples:

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Heat and Temperature Units of Heat Joule (J) – SI unit Calorie (cal) – older, not SI 1 cal = 4.184 J

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Problem Solving Analyze Read problem carefully and analyze info Plan Develop a plan to solve Compute Substitute data and conversion factors into plan and solve Evaluate Examine answers – is it reasonable? Does it make sense?

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Proportionality Variable Quantity that can change Directly proportional One goes up, other goes up; y=kx Graph – Inversely proportional One goes up, other goes down; y=k/x Graph –

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