Fundamentals of Chemistry
Unit One
Scientific Method and Measurement
Scientific Method
Scientific Method: A way to Solve
Problems.
Steps of the Scientific Method
Step 1: Identify the problem
To begin the scientific process, a
problem must be clearly and specifically
identified.
Step 2: Gather Information
Before setting out to find the answer to a
scientific question, information must be
gathered in the form of preliminary research.
Sources such as journals and scientific
papers could be checked for existing
information on the problem at hand.
Step 3: For m a Hypothesis
 Once a problem or question has been
recognized, a hypothesis or educated guess is
constructed.
 In an experiment, hypotheses are not
“correct” or “incorrect”, they are supported or
not supported by the data collected.
if a hypothesis has be tested repeatedly and
not disproven it is known as a theory or
postulate.
Theory answers the question “Why?”
(a theory explains what happened)
A rule of nature is known as a law.
Ex. Law of attraction and repulsion, Law of
universal gravitation.
Lawanswers the question “what?”
(Law tells what happens)
Step 4: Experimentation and Observation – Used
to test your hypothesis.
Data collected during this step needs to
be organized and analyzed.
-2 types of data: Qualitative & Quantitative.
▪Qualitative  made using the five senses
▪Quantitative  made using instruments
**Think about qualitative as “what”
and quantitative as “how much”
A controlled experiment contains only 1
experimental variable.
-Variable  any factor affecting the
outcome of an experiment.
▪Independent variable is set and
controlled by the experimenter
(such as time)
▪Dependent variable changes
based on what is done to the
experimental variable.
(such as plant growth)
Properly set-up experiments provide a control group
as well as an experimental group.
-Control groups are set-up under “normal”
conditions and are used to compare to the
experimental groups.
Step 5: Draw Conclusions
 interpretations of experimental results.
 reference should be made to the original
hypothesis.
Questions to think about in the conclusion may
include:
*Was the hypothesis supported or not
supported by the data?
*What were possible sources of error in
the lab?
*What are some ways to improve the
experiment?
*What are some questions yet to be addressed?
Important considerations:
1) If the data does not support the initial
hypothesis, the experiment was not
pointless!
2) If the original hypothesis or problem
addressed needs to be modified, the whole
process needs to start over.
Sometimes an experiment
that “goes wrong” opens the
doorway to a new discovery.
How Much Liquid is in Each
Graduated Cylinder?
Significant Figures: a system for
representing measured values with the
correct degree of accuracy. Its main
purpose is to know how much to round
off answers calculated from any
measurement. A "significant" figure is a
figure that is considered accurate.
Significant figures: all of the digits that are
known in a measurement plus a last digit that
is estimated.
 Measurements and calculations should
ALWAYS be recorded to the correct number
of significant figures!
 Example: Room temperature 25.4ºC
Suppose you were given temperature data
for various points in Frederick from a
variety of sources and the data looked like
this: 23.232ºC, 25.2ºC , 26.1746ºC ,
27.12ºC. When you calculate the average,
how many sig figs should keep?
3 significant figures (25.4ºC)
General Rule of Sig Figs
An answer cannot be more precise than
the least precise measurement from
which it was calculated.
RULES to identifying the number of sig. figs.:
1)Every Nonzero digit in a reported
measurement is significant
• 56.6, 2.34 and 978 all have 3 sig. figs.
2)Zeroes between nonzeroes are significant.
• 6007, 50.89 and 5.708 all have 4 sig. figs.
3)Leading zeros appearing in front of
nonzero digits are placeholders and not
considered significant.
• 0.000091, 0.042 and 0.42 all have 2 sig.figs.
4) Zeros at the end & to the right of a
decimal point are ALWAYS significant.
• 57.00, 2.030 and 7.000 all have 4 sig.
figs.
5) Zeros at the end & to the right without a
decimal point are NOT significant unless a
careful measurement was actually made
(which will have a decimal point after - 10.)
• 400, 4000 and 30000 all have 1 sig. fig.
When calculating the correct number of sig figs
in an answer, perform all of the calculations
first then round the final answer.
Summary
1. If you are not a zero, you are significant.
2. If you are a sandwiched zero, you are
significant.
3. If you are a zero at the end of a number, and
there’s a decimal in your number, you are
significant.
4. If you are a zero at the end of a number, and
there’s NOT a decimal in your number, then you
are NOT significant.
5. If you are a zero and you are at the beginning
of a number, you are NOT significant.
Adding or subtracting
 round to the same number of decimal
places as the measurement with the least
number of decimal places.
 Examples
3.451 + 1.41 + 2.072 = 6.933
6.93 (2 dec.)
7.982 + 1.02 + 2.1 = 11.102
11.1 (1 dec. )
3.45 – 1.1 = 2.35
2.4 (1 dec.)
Multiplying or dividing
round the answer to the same number of
significant figures as the measurement
with the least number of significant
figures.
examples:
2.1 x 1.301 = 2.7321
2.7
(2 sig figs)
4.02 x 2.945 = 11.8389
11.8 (3 sig figs)
0.034 x 3.223 = 0.109582
0.11 (2 sig figs)
Scientific Notation Review
Scientific Notation
A number written in scientific notation has
two components:
-a coefficient and 10 raised to a power
•Coeffiecient
 must be greater than or equal to 1 and
less than 10.
 Examples:
2.3 x 103
7.9 x 10-5
What is 540,000 in scientific notation?
-Number between 1 & 10 = 5.4
-Move the decimal 5 times
5.4 x 105
5.4
x 10 = 54
54
x 10 = 540
540 x 10 = 5,400
5,400 x 10 = 54,000
54,000 x 10 = 540,000
5.4
x 105 = 540,000
Power can be positive or negative
 positive power of ten, the decimal
moves one place to the right.
Examples: 4.67 x 103 = 4670
2.71 x 104 = 27100
negative power of ten, the decimal
point moves one place to the left.
Examples: 4.5 x 10-6 = 0.0000045
1.21 x 10-3 = 0.00121
*Remember: 10-1 = (1/10) = 0.1
3.2 x 10-1 = (3.2/10) = 0.32
Accuracy & Precision
Counting is exact!! Ex. 26 students in this class
Counted numbers are considered to have
infinite precision.
Measurements are subject to error. (Errors
reflect limitations in the methods used to make
the measurement.)
-Examples of error: incorrectly calibrated
equipment or uncertainty of equipment or
uncontrollable human error
If each of the individual measurements in a
set of data are close to the average of the set,
then they are precise.
Precision
Precision of an individual measurement is
determined by the markings on the piece of
equipment used to take the measurement.
REMEMBER: the number of significant figures
in a measurement is determined by:
-all of the known digits in the measurement
(indicated by the markings on equipment)
-plus one digit that is estimated
(how far in between the markings).
Precision Example
A thermometer marked in whole ºC and you
read it as 25.5ºC .
-you would be estimating 1 decimal
place!!
-the 25 degrees in known and the .5 is
estimated.
(It was marked to the whole degree, so
you can only estimate to the tenth.)
**Only estimate 1 place beyond what you can
read for sure!!**
Accuracy
Accuracy refers to the closeness of the
average of the set to the “accepted” value and
depends on how carefully the measurement
was made.
Example: A block of wood has a length of
4.3cm.
-Student 1 measures the length of the
block and finds it to be 4.4cm.
-Student 2 measures the block of wood and
determines its length to be 5.2 cm.
*Which measurement is more accurate?
4.4cm
Metal Ruler:
Object is more than 12.3cm
and just less than 12.4cm.
The smallest marking
represents 0.1cm, so you
estimate to the nearest
0.01cm.
The length of the object would
be accurately and precisely
recorded as 12.39cm.
The last digit is estimated, so,
12.31 – 12.39cm would be
acceptable.
Plastic Ruler:
Object is more than 12cm and less
than 12.5cm.
The smallest marking represents
0.5cm, so you estimate to the
nearest 0.1cm.
The length of the object would be
accurately and precisely recorded
as 12.4cm.
The last digit is estimated, so, 12.1
–12.4 cm would be acceptable.
(Up to 0.5 cm off)
Which ruler is more precise?
From
200.51g
to
200.57g
How much is the smallest marking worth?
0.1 gram (you can read it to the tenth’s place!!)
What are the digits of this mass you know
for certain?
200.5 grams(hundreds, tens, ones, tenths marked)
Next you always estimate 1 place beyond.
200.53 grams
Good or Poor??
Good accuracy
Poor accuracy
Good precision
Good precision
Good or Poor??
Good accuracy
(on average)
Poor precision
Poor accuracy
Poor precision
More Examples!!
Which number is more precise?
(If you were buying a gold nugget, how many
decimal places would you want to be sure of??)
A) 3.00g
B) 3.000g
C) 3g
ANSWER: B) 3.000g
Which number is a more accurate measure of a
7.00kg block? (accuracy deals with closeness!!)
A) 6.93kg
B) 6.9kg
C) 8 kg
Off by: 0.07kg
0.1kg
1kg
ANSWER: A) 6.93kg
Remember to think about accuracy ,
precision and significant digits ALL
THE TIME!!
An answer of 9.067894038399L is not
an acceptable answer in lab, test or
any other piece of paper that bears
the privilege of sporting your
signature!!
Percent Error
A mathematical value representing the
difference between the accepted value and
the experimental value.
(analyzes the accuracy of the data)
Accepted value  correct value (what the
data should be – based on reliable research)
(What you are told it should be!!)
Experimental value  value measured in lab
(what you measure or calculate it to be!!)
Formula:
% Error =
Experimental value – Accepted value x 100%
Accepted value
Negative % error  Your answer is lower
than it should be.
Positive % error  Your answer is higher
than it should be.
% Error Example 1
A block of wood has a length of 4.3cm. A
student measures the length and finds it to
be 4.4cm. What is this student’s % error?
Accepted value – experimental value x 100%
Accepted value
Experimental value = 4.4 cm (student measured)
Accepted value = 4.3cm (what you’re told it should be)
4.3cm – 4.4cm x 100% = -2.3 % error
4.3cm
% Error Example 2
A block of wood has a length of 15.8cm. A
student measures the length and finds it to
be 15.7cm. What is this student’s % error?
Accepted value – Experimental value
Accepted value
x 100%
Experimental value= 15.7 cm (student measured)
Accepted value= 15.8cm(what you’re told it should be)
15.8cm – 15.7cm x 100% = 0.63 % error
15.8cm
Metric Measurements
SI (International System of units) system is
used worldwide based on units of ten.
Base Unit Abbreviation
Meter
m
Second
s
Kelvin
K
Gram
g
Ampere
A
Candela
Cd
Mole
Mol
Quantity Measured
Length
Time
Temperature
Mass
Electric current
Luminous intensity
Amount of substance
All other units are derived from the seven
base units (thus known as derived units).
Volume: The amount of space an object
occupies.
Can be determined by three methods:
1. Formula: volume=ℓ x w x h
(units= cm3)
2. Measuring with a graduated cylinder
(units = mL)
3. Determined by water displacement
(units = mL = cm3)
Remember that 1 mL = 1 cm3
If a metal block displaces 8.0mL of water,
then the block’s volume in cm3 is 8.0cm3.
* What is the volume in cm3 of a metal toy
that displaces 7.5mL of water when
dropped into a small container?
7.5cm3
Mass  A measure of the amount of
matter in an object.
Measured on a balance. (ex. Triple beam balance,
digital or electronic balance)
Weight  A measure of the force of gravity acting
on an all objects with mass. The product of mass
and gravitational force.
Density  The amount of mass per unit of volume.
 formula: density=mass/volume
D = m/V
Temperature  A measure of the
average kinetic energy of the particles
in a sample of matter.
 The scales are used to measure
temperature are Fahrenheit, Celsius and
Kelvin.
 Kelvin is the SI unit for temperature.
Using Prefixes
The distance form Maryland to Utah
would be best measured in km.
The length of a pencil would be
measured in cm.
The height of the letter “h” would be
measured in mm.
** Different prefixes are used for
different amounts**
Prefix
Mega
Kilo
Hecta
Deka
Base unit
Deci
Centi
Milli
Micro
Nano
Pico
Symbol
M
k
h
dk
d
c
m
μ
n
p
# base units
One million
One thousand
One hundred
Ten
One
One tenth
One hundredth
One thousandth
One millionth
One billionth
One trillionth
Sci. Notation
1 x 106
1 x 103
1 x 102
1 x 101
1 x 100
1 x 10-1
1 x 10-2
1 x 10-3
1 x 10-6
1 x 10-9
1 x 10-12
Conversions
To convert between units, you could move
the decimal point. (if factors of ten!!)
_____  ____
0.0004
0.004  ____
0.04  0.4  4  40  400
K
h
dk
U
d
c
m
5  50  500  5000  50000
_____ 500000
______ 5000000
_____
Dimensional Analysis (factor-label method)
 used to convert from units
1) write down what is known (number & unit)
2) set up a conversion factor with the target
end unit on top and one known unit on the
bottom (if unit you are canceling is on top)
3) divide the product of the numbers in the
numerator by the product of the numbers in
the denominator
4) make sure that the final answer has the
same number of significant figures as the
number given.
Examples
#1. How many seconds are in 7 minutes?
known = 7 min.
conversion factor = 60 sec. / 1 min.
7 min x 60 sec = 420 sec = 420 sec
1 min
1
Examples
#2. How many cm are there in 5.2 meters?
known = 5.2 m
conversion factor = 1 m / 100 cm
5.2 m x 100 cm = 520 cm = 520 cm
1m
1
Examples
#3. How many hours are there in 3 weeks?
known = 3 wk
conversion factor = 1 wk / 7 days
1 day / 24 hr
3 wk x 7 days x 24 hr = 520 hr = 520 hr
1 wk
1 day
1