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 –