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Scientific
Method
Mass vs. Weight
• First we will define Matter…
– Matter – anything that has mass & takes
up space
• Mass – measurement that tell how
much matter you have (kg)
• Weight – measurement of the amount
of matter you have with the effect of
gravity
For Example…
• Let’s say a guy weighs 150 pounds
• This is about 54 kg in mass
• What would his mass be on the moon if
the moon’s gravity is about 1/6 that of
the Earth?
Hmmmm…
•
•
•
•
Would it be 1/6 of 150 pounds?
Would it be 1/6 of 54 kg?
Would it be 150 pounds
Or would it be 54 kg?
The answer is …
54 kg
Some of you are scratching your
heads…
• The reason is because gravity has
NOTHING to do with mass – that’s only
for weight
• His mass did not change only his weight
changed
The Scientific Method
• Scientific Method – a systematic
approach used in scientific study
• It is an organized approach for
scientists to do research
• Provides a method for scientists to
verify their work and the work of others
Steps for the Scientific Method
Step # 1 – Observation
• Observation – the act of gathering
information (data)
– Qualitative data – information with NO
numbers
• (hot, blue, rainy, cold)
– Quantitative data – information with
numbers
• (98°F, 80% humidity, 0°C)
Steps for the Scientific Method
Step # 2 – Form a Hypothesis
• Hypothesis – tentative explanation for
what has been observed
– There is no formal evidence at this point
– It is just a gut feeling
Steps for the Scientific Method
Step # 3 – Experimentation
Experimentation – a set of controlled
observations that test the hypothesis
– Independent variable – the thing that you
change in the experiment
– Dependant variable – the thing that
changes because you changes the
independent variable
– Constant – something that does not
change during the experiment
– Control – the standard for comparison
For example…
• Let’s say we are going to do an
experiment testing what happens when
you heat and cool a balloon…
We will start with a balloon at
room temperature
Now we will change something…
I will add heat
to one balloon
It will expand
What will happen
to the balloon’s
size?
Now let’s cool things down
I will add cool
down the
balloon
It will get
smaller
What will happen
to the balloon’s
size?
So what is what?
• What variable did YOU change?
– Temperature (Independent Variable)
• What variable changes BECAUSE you
changed the temperature?
– Size of the balloon (Dependent Variable)
• What is did not change in the experiment?
– Amount of air in the balloon, what the balloon is
made of… (Constant)
• What balloon did you use to compare the
others to?
– The room temperature balloon
(Control)
Steps for the Scientific Method
Step # 4 – Conclusion
• Conclusion – judgment based on the
information obtained
Introduction to Significant
Figures
&
Scientific Notation
Significant Figures
• Scientist use significant figures to
determine how precise a measurement
is
• Significant digits in a measurement
include all of the known digits plus one
estimated digit
For example…
• Look at the ruler below
• Each line is 0.1cm
• You can read that the arrow is on 13.3 cm
• However, using significant figures, you must
estimate the next digit
• That would give you 13.30 cm
Let’s try this one
• Look at the ruler below
• What can you read before you
estimate?
• 12.8 cm
• Now estimate the next digit…
• 12.85 cm
The same rules apply with all
instruments
• The same rules apply
• Read to the last digit that you know
• Estimate the final digit
Let’s try graduated cylinders
• Look at the graduated cylinder below
•
•
•
•
What can you read with confidence?
56 ml
Now estimate the last digit
56.0 ml
One more graduated cylinder
• Look at the cylinder below…
• What is the measurement?
• 53.5 ml
Rules for Significant figures
Rule #1
• All non zero digits are ALWAYS
significant
• How many significant digits are in the
following numbers?
•274
•3 Significant Figures
•25.632
•5 Significant Digits
•8.987
•4 Significant Figures
Rule #2
• All zeros between significant digits are
ALWAYS significant
• How many significant digits are in the
following numbers?
504
3 Significant Figures
60002
5 Significant Digits
9.077
4 Significant Figures
Rule #3
• All FINAL zeros to the right of the
decimal ARE significant
• How many significant digits are in the
following numbers?
32.0
3 Significant Figures
19.000
5 Significant Digits
105.0020
7 Significant Figures
Rule #4
• All zeros that act as place holders are
NOT significant
• Another way to say this is: zeros are
only significant if they are between
significant digits OR are the very final
thing at the end of a decimal
For example
How many significant digits are in the following numbers?
0.0002
6.02 x 1023
100.000
150000
800
1 Significant Digit
3 Significant Digits
6 Significant Digits
2 Significant Digits
1 Significant Digit
Rule #5
• All counting numbers and constants
have an infinite number of significant
digits
• For example:
1 hour = 60 minutes
12 inches = 1 foot
24 hours = 1 day
How many significant digits
are in the following numbers?
0.0073
100.020
2500
7.90 x 10-3
670.0
0.00001
18.84
2 Significant Digits
6 Significant Digits
2 Significant Digits
3 Significant Digits
4 Significant Digits
1 Significant Digit
4 Significant Digits
Rules Rounding Significant
Digits
Rule #1
• If the digit to the immediate right of the last
significant digit is less that 5, do not round up
the last significant digit.
• For example, let’s say you have the number
43.82 and you want 3 significant digits
• The last number that you want is the 8 –
43.82
• The number to the right of the 8 is a 2
• Therefore, you would not round up & the
number would be 43.8
Rounding Rule #2
• If the digit to the immediate right of the last
significant digit is greater that a 5, you round
up the last significant figure
• Let’s say you have the number 234.87 and
you want 4 significant digits
• 234.87 – The last number you want is the 8
and the number to the right is a 7
• Therefore, you would round up & get 234.9
Let’s try these examples…
200.99
(want 3 SF)
201
18.22
(want 2 SF)
18
135.50
(want 3 SF)
136
0.00299
(want 1 SF)
0.003
98.59
(want 2 SF)
99
Significant Digits
Calculations
Significant Digits in
Calculations
• Now you know how to determine the
number of significant digits in a number
• How do you decide what to do when
adding, subtracting, multiplying, or
dividing?
Rules for Addition and
Subtraction
• When you add or subtract measurements,
your answer must have the same number of
decimal places as the one with the fewest
• For example:
20.4 + 1.322 + 83
= 104.722
Addition & Subtraction
Continued
• Because you are adding, you need to look at the
number of decimal places
20.4 + 1.322 + 83 = 104.722
(1)
(3)
(0)
• Since you are adding, your answer must have the
same number of decimal places as the one with the
fewest
• The fewest number of decimal places is 0
• Therefore, you answer must be rounded to have 0
decimal places
• Your answer becomes
• 105
Addition & Subtraction
Problems
1.23056 + 67.809 =
69.03956  69.040
23.67 – 500 =
- 476.33  -476
40.08 + 32.064 =
72.1440  72.14
22.9898 + 35.453 =
58.4428  58.443
95.00 – 75.00 =
20  20.00
Rules for Multiplication & Division
• When you multiply and divide numbers
you look at the TOTAL number of
significant digits NOT just decimal
places
• For example:
67.50 x 2.54
= 171.45
Multiplication & Division
• Because you are multiplying, you need to look at the
total number of significant digits not just decimal places
67.50 x 2.54 = 171.45
(4)
(3)
• Since you are multiplying, your answer must have the
same number of significant digits as the one with the
fewest
• The fewest number of significant digits is 3
• Therefore, you answer must be rounded to have 3
significant digits
• Your answer becomes
• 171
Multiplication & Division
Problems
890.15 x 12.3 =
10948.845  1.09 x 104
88.132 / 22.500 =
3916.977  3917.0
(48.12)(2.95) =
141.954  142
58.30 / 16.48 =
3.5376  3.538
307.15 / 10.08 =
30.47123  30.47
More Significant Digit
Problems
18.36 g / 14.20 cm3
= 1.293 g/cm3
105.40 °C –23.20 °C
= 82.20 °C
324.5 mi / 5.5 hr
= 59 mi / hr
21.8 °C + 204.2 °C
= 226.0 °C
460 m / 5 sec
= 90 or 9 x 101 m/sec
Scientific Notation
• Scientific notation is used to express
very large or very small numbers
• I consists of a number between 1 & 10
followed by x 10 to an exponent
• The exponent can be determined by the
number of decimal places you have to
move to get only 1 number in front of
the decimal
Large Numbers
• If the number you start with is greater than 1,
the exponent will be positive
• Write the number 39923 in scientific notation
• First move the decimal until 1 number is in
front – 3.9923
• Now at x 10 – 3.9923 x 10
• Now count the number of decimal places that
you moved (4)
• Since the number you started with was
greater than 1, the exponent will be positive
• 3.9923 x 10 4
Small Numbers
• If the number you start with is less than 1, the
exponent will be negative
• Write the number 0.0052 in scientific notation
• First move the decimal until 1 number is in
front – 5.2
• Now at x 10 – 5.2 x 10
• Now count the number of decimal places that
you moved (3)
• Since the number you started with was less
than 1, the exponent will be negative
• 5.2 x 10 -3
Scientific Notation Examples
Place the following numbers in scientific notation:
99.343
9.9343 x 101
4000.1
4.0001 x 103
0.000375
3.75 x 10-4
0.0234
2.34 x 10-2
94577.1
9.45771 x 104
Going from Scientific Notation
to Ordinary Notation
• You start with the number and move the
decimal the same number of spaces as
the exponent.
• If the exponent is positive, the number
will be greater than 1
• If the exponent is negative, the number
will be less than 1
Going to Ordinary Notation
Examples
Place the following numbers in ordinary notation:
3 x 106
6.26x 109
5 x 10-4
8.45 x 10-7
2.25 x 103
3000000
6260000000
0.0005
0.000000845
2250
Conversions
And Density Problems
Accuracy vs. Precision
• Accuracy – How close you are to the
correct answer
• Precision – How close your answers
are together
For Example…
• Let’s say we had the following dart
board
Is the accuracy good or bad?
Accuracy - GOOD
Is the precision good or bad?
Precision - GOOD
Try this one
• Let’s say we had the following dart
board
Is the accuracy good or bad?
Accuracy - BAD
Is the precision good or bad?
Precision - GOOD
Try this one
• Let’s say we had the following dart
board
Is the accuracy good or bad?
Accuracy - BAD
Is the precision good or bad?
Precision - BAD
Dimensional Analysis
• Dimensional analysis is just a big word
for going from one unit to another.
• Have you ever converted inches into
feet or years into days?
• If so, then you have done dimensional
analysis
Dimensional Analysis
• Dimensional Analysis – method of problemsolving that focuses on changing units
• Conversion Factor – a ratio of equal values
used to go from one unit to another
– Example: 1 foot = 12 inches
– Can be written as 1 foot
12 inches
Rules for Dimensional Analysis
1.
2.
3.
4.
ALWAYS start with the given!!!
Draw a multiplication sign and a line
Place the unit to be canceled on the bottom
Place a conversion factor on the line you
have drawn
5. Cross out units and see what you have left.
6. You must have one on top & one on the
bottom
A/ x B
A/
Let’s try an example…
Let’ s convert 32.5 inches to feet.
1. Start with your given
32.5 inches
2. Draw your line and multiplication sign
32.5 inches x ___________
3. Put the unit to be crossed out on the bottom
32.5 inches x __________
inches
4. Write a conversion factor to switch units
32.5 inches x __1_foot___
12 inches
Keep going…
5. Cross out top and bottom units
/
32.5 inches x __1_foot___
12 inches
/
6. Are you left with the unit that you
wanted?
YES
7. If so, work the problem & you are done
/
32.5 inches x __1_foot___ = 2.70833 feet
12 inches
/
You’re not really done yet…
• What did we forget?
– SIGNIFICANT DIGITS !!!
• What operation are we doing?
– Multiplication
• So what do we look at?
– The total number of Sig. Figs
• Our answer should have the same number of
Sig. Figs as the given, which in this case is 3
• The answer becomes…
2.71 feet
Try this example…
• How many seconds are in 82.95
minutes?
• Start with the given
82.95 minutes
• Draw your line
82.95 minutes x ___________
• Place the unit to be crossed out on the
bottom
82.95 minutes x ___________
minutes
Keep going…
• Place the conversion factor on the line
82.95 minutes x _60 seconds_
1 minute
• Cross out the units
/
82.95 minutes x _60 seconds_
1 minute
/
• Are you left with the unit you wanted?
Yes!
• Just work the problem & check Sig. Figs
82.95 minutes x _60 seconds_ = 4977 seconds
1 minute
What if you need to Change 2
Units?
Convert 65 miles per hour to kilometers per
second
(0.625 miles = 1 Km)
Start with your given
65 miles x 1 km x 1 hr x 1 min = 0.029 Km / sec
1 hour
0.625 mi 60 min
60 sec
Conversions with Prefixes
• Conversions with prefixes are done in
exactly the same manner
• You just have to know the prefixes
Prefixes
Prefix
Symbol
Value
Giga
G
1 x 10 9
Mega
M
1 x 10 6
Kilo
K
1 x 10 3
Deci
d
1 x 10 - 1
Centi
c
1 x 10 - 2
Milli
m
1 x 10 - 3
Micro
µ
1 x 10 - 6
Nano
n
1 x 10 - 9
Pico
P
1 x 10 - 12
Femto
f
1 x 10 - 15
Rules with Prefixes
•
•
•
•
•
The rules are the same…
Start with the given
Place the cross out unit on the bottom
Place conversion unit on top
Keep crossing out until you get what
you want
A few differences
• Always remember that the # 1 will go
with your Prefix
• The number with in scientific notation
will go with your base unit
• You can only go from a prefix to a base
unit
Let’s try one
• Convert 100 nm into m
Start with your given
100 nm x 1 x 10 -9 m = 1 x 10 – 7 m
1 nm
Try this one…
• Convert 785 mm to km
785 mm x 1 x 10 -3 m x
1 mm
1 km
1 x 10 3 m
= 7.85 x 10 – 4 km
Temperature Conversions
• The three units for measuring
temperature are…
– Celsius
– Fahrenheit
– Kelvin
To Convert Among Temperatures
Use These Formulas
• ºF = 1.8 ºC + 32
• ºC = 0.56 (ºF – 32)
• K = ºC + 273
Try these examples
•
•
•
•
Convert 35 °C to Kelvin
K = ºC + 273
K = 35 + 273
K = 308 K
Example
•
•
•
•
Convert 55 ºC to ºF
ºF = 1.8 ºC + 32
ºF = 1.8 (55) + 32
ºF = 131 = 130 ºF
Example
•
•
•
•
Convert 95.8 ºF to ºC
ºC = 0.56 (ºF – 32)
ºC = 0.56 (95.8 – 32)
ºC = 35.7 ºC
Example
• Convert 75.0 °F to Kelvin
• You must first convert to °C and then go
to Kelvin
• ºC = 0.56 (ºF – 32)
• ºC = 0.56 (75 – 32)
• ºC =24.1 ºC
• K = ºC + 273
• K = 24 + 273
• K = 297 K
Density
• Density - mass per unit volume
(g/cm3)
M
D=
V
M
D V
Density
• An object has a volume of 825 cm3 and a
density of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
M=?
M = DV
M
D V
M = (13.6 g/cm3)(825cm3)
M = 11,220 g = 11,200 g
Density
A liquid has a density of 0.87 g/mL. What
volume is occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
M = 25 g
V=M
D
M
D V
V=
25 g
0.87 g/mL
V = 28.7 mL = 29 mL
Density
You have a sample with a mass of 620 g & a
volume of 753 cm3. Find density.
GIVEN:
WORK:
M = 620 g
V = 753 cm3
D=?
D=M
V
M
D V
D=
620 g
753 cm3
D = 0.82 g/cm3
Density
• The good thing about density is that it is
an intensive property
• That means that the density of a
substance is the same regardless of the
amount
• If you find the density of an unknown
material, you can look it up in a density
chart to find its identity
Density
• I have a block that measures 5.25 cm
by 2.25 cm by 8.50 cm.
• I weigh the block and find its mass to be
5.85 g
• Calculate the density of the block in
g/cm3
Density
•
•
•
•
•
•
•
•
•
•
D=M/V
We know the mass and we want to find the density.
Therefore we must also find the volume.
How do you find the volume of a cube?
V cube = l x w x h
V cube = (5.25) x (2.25) x (8.50) = 100.4 cm3
Now we can calculate the density
D=M/V
D = 5.85 g / 100.4 cm3
0.0583 g / cm3
What of you have an odd shaped
object?
• The density of an odd shaped object can be found by
the same equation
• D=M/V
• To find the mass, you just weigh the odd shaped
object
• To find the volume, you place water in a graduated
cylinder and get an initial volume
• Then you place the object into the graduated
cylinder.
• The volume of the object is the difference in the two
volumes
For example
• A chunk of metal has a mass of 5.25 g. It is
placed in a graduated cylinder containing
25.0 ml of water. Once the metal is placed in
the graduated cylinder, the water rises to 38.2
ml. What is the density of the metal?
• M = 5.25 g
• V = 38.2-25.0 = 13.2 ml
• D = M / V = 5.25 g / 13.2 ml = 0.398 g / ml