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 TeraTTerameter GigaGGigameter MegaMMegameter KiloK or kKilometer HectoHHectometer DecaDDecameter meter DecidDecimeter CenticCentimeter MillimMillimeter MicroµMicrometer NanonNanometer PicopPicometer 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

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 = 4 SF  Sandwich zeros ARE significant 306 = 3 SF  Leading zeros ARE NOT significant = 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)  (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 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 …3.79 5, not followed by nonzero digit and preceded by odd digit(s) increase last digit by 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 – memorize!!  °C = K –  Examples:

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