Data Analysis
Chapter 2
2.1 SI Units
SI – International System of Units
- standard units of measurement for scientists
SI Base Units:
Time - second (s)
Length – meter (m)
Mass – kilogram (kg)
Temperature – Kelvin (K)
Amount – mole (mol)
2.1 SI unit
Derived Units – a unit that is defined by a
combination of base units
Volume is a derived unit:
V = l x w x h (units for volume are cm3 or ml)
Density is a derived unit:
D=
m ass( g )
volum e(m l)
SI Prefixes
Prefix
Factor
Conversion Factor
1000 times larger
1 km = 1000 m
hecta (h)
100 times larger
1 hm = 100 m
Deca (D)
10 times larger
1 Dm = 10 m
kilo
(k)
BASE UNIT L, m, g
deci (d)
10 times smaller
10 dm = 1 m
centi (c)
100 times smaller
100 cm = 1 m
milli
1000 times smaller
1000 mm = 1 m
(m)
Temperature
The SI unit for temperature is Kelvin (K).
To convert from Celsius to Kelvin:
from Celsius  to Kelvin ADD 273
from Kelvin  to Celsius SUBTRACT 273
Example:
No degree
- 39°C 
K
symbol for
332 K 
°C
Kelvin
Homework
Pg. 30 # 4, 5, 7, 8, 9, 11
Pg. 50 # 51- 57
2.1 Density
Density =
m ass( g )
volum e(m l)
Example: solve for density
mass = 13.5 g ; volume = 5.0 cm3
D = 2.7 g/cm3
Density
Examples:
1. Solve for volume
mass = 12.4 g ; density = 25.4 g/ml
2. Solve for mass
density = 425 g/ml ; volume = 1.36 ml
Density
Examples: try yourself
1. Solve for density
mass = 7.5 g ; volume = 13.2 ml
2. Solve for mass
density = 0.5 g/cm3 ; volume = 32.5 cm3
Homework
Pg. 29 # 1, 2, 3
Pg. 30 # 6, 10
2.2 Scientific Notation
Scientific Notation – way to express very large
and very small numbers
Written as:
A number 1 - 9.99 X 10x
raised to a power
- the exponent tells you how many times the
number is multiplied by 10
Example: 3.14 x 103 or 3.14 x 10-3
2.2 Scientific Notation
When the number is larger than 1 then the
exponent will be positive
Example:
542000 = 5.42 x 105
When the number is less than 1 then the
exponent will be negative
Example:
0.0023 = 2.3 x 10-3
2.2 Scientific Notation
Example: Write the following in scientific notation
56300000 =
0.0018 =
0.00000794 =
Example: Write the following in standard form
2.7 x 106 =
3.54 x 103 =
7.8 x 10-4 =
2.2 Scientific Notation
Examples : Try these yourself
0.00254 =
1.5 x 10-4 =
187000 =
9.14 x 106 =
6.3 x 10-2 =
0.00360 =
2.3 Reliable Measurements
Accuracy – refers to how close a measured
value is to an accepted value
Precision – refers to how close a series of
measurements are to one another
Use mini golf example:
Whose score is the most accurate?
Whose score is the most precise?
Whose score is the most accurate and precise?
2.3 Significant Figures




How precise are your measuring devices?
Which is more precise, a clock or a
stopwatch?
In science we use digits to describe precision.
The digits reported are called significant
figures.
2.52 g is more precise than 2.5 g
Significant Figures include all known digits plus
one estimated digit.
2.3 Significant Figures
Example Ruler:
2.3 Significant Figures
Rules for recognizing significant figures:
Use these rules for telling how many sig figs
are in a number.
1. Non zero numbers are always significant
Ex: 72.3 
3 sig figs
2. Zeros between non-zero numbers are
always significant
Ex: 6023.5  5 sig figs
2.3 Significant Figures
3. All final zeros to the right of the decimal
place are significant
Ex: 25.30  4 sig figs
4. Zeros that act as placeholders are NOT
significant
Ex: 0.025 & 430  2 sig figs
5. Counting numbers, constants, and
conversion factors have an infinite number
of sig. figs.
Ex: 6 atoms  infinite # of sig figs
2.3 Significant Figures
United States Method for Sig Figs:
Pacific =
decimal
present
Atlantic =
decimal
absent
2.3 Significant Figures
Reporting your Answer with the correct number
of significant figures:
When you multiply or divide numbers your
answer must have the same number of sig
figs as the measurement in the problem with
the fewest sig figs.
Example:
3.0 x 2.54 =
320 / 12.54 =
Dimensional Analysis
Conversional factor – ratio of equivalent values
used to express the same quantity in different
units.
Ex: 60 sec
1m
1000g
1 min
100 cm
1kg
Dimensional Analysis – method of problem
solving that focuses on the units used
Dimensional Analysis
Steps for solving problems using dimensional
analysis
1. Put the number they give you (w/ units) over 1
2. Set up your next fraction line
3. Put the units you started with in the denominator
4. Put the units you want in the numerator (top)
- always go back to the base if it is not in the
problem
Dimensional Analysis
5. Put a # 1 in front of the larger unit
6. Put the number of smaller units that is equal
to 1 of the bigger unit
7. Multiply across the top, multiply across the
bottom and then divide your answers
8. Write your answer with sig figs and units
Dimensional Analysis
Examples:
How many seconds are in 3 minutes?
How many meters are in 45.6 cm?
Dimensional Analysis
Examples:
Convert 3.2 ml to L.
Convert 16.2 g to dg.
Dimensional Analysis
Examples – 2 step problems
Convert 54 cm to km.
Convert 4.0 x 10-3 Dg to mg.