# CHAPTER 2 Measurements and Calculations. Scientific Method System  Specific portion of matter that has been selected for study Scientific Method  Logical.

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CHAPTER 2 Measurements and Calculations

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

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

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

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

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

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!!!

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

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

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

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

Measuring Always estimate one more place than the measuring device

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

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

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

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

Significant Figures Exact numbers -

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

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

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

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

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

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

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

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

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:

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

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?

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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