Measurements and Calculations CHAPTER 2 Measurements and Calculations

Scientific Method System Scientific Method 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 Organizing – Graphs, tables, statistics Hypothesis – testable statement Law – statement that DESCRIBES facts

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

Units of Measurement Unit of Measurement SI 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 Length – meter (m) Mass – gram (g) Time – second (s) Temperature – Kelvin (K)

Know the ones in BOLD above!!! SI Prefixes Prefix Symbol Example Exponential Factor Factor Tera T Terameter 1012 1000000000000 Giga G Gigameter 109 1000000000 Mega M Megameter 106 1000000 Kilo K or k Kilometer 103 1000 Hecto H Hectometer 102 100 Deca D Decameter 101 10 ---- meter Deci d Decimeter 10-1 0.1 Centi c Centimeter 10-2 0.01 Milli m Millimeter 10-3 0.001 Micro µ Micrometer 10-6 0.000001 Nano n Nanometer 10-9 0.000000001 Pico p Picometer 10-12 0.000000000001 Know the ones in BOLD above!!!

SI Prefixes Number Line – MEMORIZE!! K H D d c m _ _ µ_ _ n Examples:

Derived SI Units Derived Unit – obtained from combining base units Area L * w ; m2 Volume L * w * h ; m3 Speed Length/time ; m/s Density Mass/volume ; g/mL or g/cm3

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

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

Significant Figures Sig Figs – all certain digits plus one uncertain digit 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: To the left – ARE NOT significant unless a special sign 300 = 1 SF 300. = 3 SF To the right – ARE significant 0.02300 = 4 SF Scientific Notation All digits in the number portion ARE significant 2.31 x 103 = 3 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 – Decide where the number will be “cut” Look at number to the right: If it is a 5 or greater, increase the number by one If it is less than 5, leave number as is

Significant Figures Examples:

Scientific Notation Used to represent very big or very small numbers Generic form: M x 10N 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 Example: 4.21 x 102  4.21 = number part in standard form (one digit to left of decimal point)  102 = tells where decimal is  2 = exponent

Scientific Notation Converting TO Scientific Notation Count the number of spaces needed to get into PROPER form. This becomes the exponent. Moving the decimal point left means N is +. Moving the decimal point right means N is -. Examples:

Scientific Notation Converting OUT OF scientific notation: Move the decimal the number of spaces indicated by the exponent (the number), the correct direction, also indicated by the exponent (the sign) Examples:

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

Scientific Notation Math and scientific notation Add/Subtract Multiply 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 Heat 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

Heat and Temperature Kelvin Freezing point of water = 273 K Boiling point of water = 373 K K = °C + 273.15 °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 Plan Compute Evaluate 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 Directly proportional Inversely proportional 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