chapter 2 measurements and calculations. scientific method system specific portion of matter that...
TRANSCRIPT
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 Organizing – Graphs, tables, statistics Hypothesis – testable statement Law – statement that DESCRIBES facts
Scientific Method
Steps Theorizing
Statements 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 Length – meter (m) Mass – gram (g) Time – second (s) Temperature – Kelvin (K)
SI PrefixesPrefix Symbol Example Exponential
FactorFactor
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 100 ----
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
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
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 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 –