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
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
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!!
KHD
With meters:
Examples:
dcm__µ
Derived SI Units

Derived Unit – obtained from combining
base units

Area



Volume



L*w*h
m3
Speed



L*w
m2
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


Conversion Factors = 1
Examples:
Using Scientific
Measurements

Accuracy


Precision


Closeness of a measurement to the true or
accepted value
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


Sandwich zeros ARE significant


.000239 = 3 SF
Trailing zeros:


306 = 3 SF
Leading zeros ARE NOT significant


3.456 = 4 SF
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 103 = 3 SF
3.0 x 103 = 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 digit
12.02 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 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
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



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



Multiply


Exponents MUST be the same!!
Add M values and exponent stays the same
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


Plan


Develop a plan to solve
Compute


Read problem carefully and analyze info
Substitute data and conversion factors into plan
and solve
Evaluate

Examine answers – is it reasonable? Does it
make sense?
Proportionality

Variable


Directly proportional



Quantity that can change
One goes up, other goes up; y=kx
Graph –
Inversely proportional


One goes up, other goes down; y=k/x
Graph –