The Wonderful World of
Metrics!
Introduction
 The metric system is a different
way of measuring things. The
practice is the same, but different
units are involved.
 Can you think of any metric
measurements that you have seen
or heard?
The “Basics”
 The metric system uses SI base units as a
foundation. Those units are…..
 Meter (m) – a measure of distance
 Liter (L) – a measure of volume
 Kilogram (kg) – a measure of mass

(this is the only one that uses a prefix! More on that soon…)
 Second (s) – a measure of time
 Kelvin (K) – a measure of temperature
 Mole (mol) – a measure of an amount
The “Basics”
 Every measurement will include one
of the base words.
 The metric system uses Prefixes too.
 Every prefix is related to the base
units. But how is that possible…
Pioneering the Prefixes
 Lets start with the prefixes for large measurements….
 KILO (k)
 HECTO (h)
 DECA (da)
1 kilometer = 1000 meters
1 Hectoliter = 100 liters
1 Decagram = 10 grams
 Remember Meters, Liters, Grams, and Seconds are
the base units. They will be in every measurement.
Pioneering the Prefixes
 How about the small measurements…
 DECI (d) – 1 decimeter = 1/10 meter
 CENTI (c) – 1 centiliter = 1/100 liter
 MILLI (m) – 1 milligram = 1/1000 gram
 Remember, these prefixes are always added to the
base root word
 But that’s so confusing….isn’t there an easierr way to
remember all this?
Good ol’ King Henry
King Henry Died by Drinking Chocolate Milk
Kilo
Hecto
Deca
Base
Deci
Centi
Milli
Can you Think of your own?
Converting Skillz
 When you are converting from one unit to another
unit


First figure out what you are starting with
Then where (which direction) you are going!
 If you move to the right (aka big to small) then you
move the decimal to the right.
 If you move to the left (aka small to big) then you
move the decimal to the left.
Practice makes Perfect!
Try this one.
1 meter =
hectometer
1st- Figure out your starting point and where you are
going!
K h da b d c m
2nd – Find the Decimal and move it the same way and
number you moved in step 1.
Practice makes Perfect!
And this one.
2.5 kilograms =
grams
1st- Figure out your starting point and where you are
going!
K h da b d c m
2nd – Find the Decimal and move it the same way and
number you moved in step 1.
Practice makes Perfect!
Last one!
17.504 deciliters =
decaliters
1st- Figure out your starting point and where you are
going!
K h da b d c m
2nd – Find the Decimal and move it the same way and
number you moved in step 1.
Precision vs Accuracy
 Precision
 A measure of the degree to which the measurements made (and
made in the same way) agree with each other
 Accuracy
 Degree to which the experimental value agrees with the true or
accepted value
 So, can measurements be precise without being
accurate?
Precision vs Accuracy
Density
Comparing Feathers and Rocks
 Which do you think would have the greater mass?
 Which do you think would have the greater volume?
 1 kg of feathers
 1 kg of rock
Density
 Density is defined as mass per unit volume.


Density is a measure of how tightly packed molecules are
in an object.
Basically, it is the amount of matter within a certain
volume.
The Math…
 The Units:
 Mass = Grams (g)

Volume (2 ways)
Ruler = cm3
 Displacement = ml


Density (2 ways)
Ruler = g/cm3
 Displacement = g/ml

What is Density?
If you take the same volume of different substances, then
they will weigh different amounts.
Water
Iron
1
cm3
1
cm3
1
cm3
0.50 g
1.00 g
8.00 g
Wood
Q) Which of these is most dense? Why?
IRON!
It has the most mass for
that volume.
Density for different things…
Substance
 Each substance has it’s
own density.
 It does not matter how
much of a substance you
have, it will have the same
density.
1 gram of water will have the
same density as 100 grams
of water
 Distilled Water has a density
of 1 g/cm3

(This is the only density you need to memorize!)
Hydrogen
Helium
Air (atmospheric air)
Carbon Monoxide
Carbon Dioxide
Gasoline
Ice
Water (@ 20deg C)
Water (@ 4deg C)
Milk
Magnesium
Water in the Dead Sea
(31.5% salt in the water)
Aluminum
Iron
Lead
Mercury
Gold
Lead
Density (g/cm3)
0.00009
0.000178
0.001293
0.00125
0.001977
0.70
0.922
0.998
1.000
1.03
1.07
1.24
2.7
7.8
11.3
13.6
19.3
21.4
Density for different things…
Substance
 Objects with different densities
interact in a very predictable way
The more dense object will sink, the
less dense will rise to the top…

Density
(g/cm3)
Hydrogen
Helium
Air (atmospheric air)
Carbon Monoxide
Carbon Dioxide
Gasoline
Ice
Water (@ 20deg C)
Water (@ 4deg C)
Milk
Magnesium
Water in the Dead Sea
(31.5% salt in the water)
Aluminum
Iron
Lead
Mercury
0.00009
0.000178
0.001293
0.00125
0.001977
0.70
0.922
0.998
1.000
1.03
1.07
1.24
Gold
Lead
19.3
21.4
2.7
7.8
11.3
13.6
Different objects have different densities
 Is the ice or the water more dense?
 The water is more dense than the
ice because the ice floats!
 Objects with more than 1 g/cm3
density will sink in tap water (ex: gold
at 19.3)
 Objects with less than 1 g/cm3 density
will float in tap water (ex: ice at 0.93)
Sidenote…
Sulfur hexaflouride. Density? Explain this.
The Math…
 The Units:
 Mass = Grams (g)

Volume (2 ways)
Ruler = cm3
 Displacement = ml


Density (2 ways)
Ruler = g/cm3
 Displacement = g/ml

Determining Density
Step 1:
Find the mass of the object
Determining Density
 STEP 2: Determine Volume
 We have 2 ways to determine VOLUME.
 Measure
Cube = L * W * H
 Cylinder = Πr2H
 Sphere = (4Πr3)/3


Calculate Displacement

Displacement is how much liquid is moved out of the way to make
room for the object placed in water
Determining Density
Step 3:
Calculate
Density = Mass
Volume
Units:
For ruler: g/cm3
For displacement: g/ml
To find density:
1)
Find the mass of the object
2)
Find the volume of the object
3)
Divide : Density = Mass / Volume
Ex. If the mass of an object is 35 grams and it takes up 7 cm3 of
space, calculate the density.
To find density:
1)
Find the mass of the object
2)
Find the volume of the object
3)
Divide : Density = Mass / Volume
Ex. If the mass of an object is 35 grams and it takes up 7 cm3 of
space, calculate the density.
Set up your density problems like this:
Known: Mass = 35 grams
Volume = 7 cm3
Unknown: Density (g/cm3)
Formula: D = M / V
Solution: D = 35g / 7cm3
D = 5g/cm3
Practice Problem 1
Osmium is a very dense metal. What is its
density in g/cm3 if 50.00 g of the metal occupies
a volume of 2.22cm3?
1)
2)
3)
2.25 g/cm3
22.5 g/cm3
111 g/cm3
Practice Problem #3
17
What is the density (g/cm3) of 48 g of a metal if the
metal raises the level of water in a graduated
cylinder from 25 mL to 33 mL?
A) 0.2 g/ cm3
B) 6 g/cm3
C) 252 g/cm3
25 ml
lecturePLUS Timberlake
33 mL
The Nature of Science
(How Scientists Think)
Why Science?

The goal of science is to understand the
natural world we live in.
Why Hypothesize?

Scientist hypothesize in order to try to
explain what they think will happen in a
certain situation
Long-held assumptions should be questioned!
How do you achieve Scientific
success?
Be creative: think outside the box!
 Those “Creative” experiments end up being
the best ones.


Persevere:
If at first you don’t succeed, try, try, try again!
 If you did succeed, do it again to make sure it
was correct in the first place.


Question everything, but make your
questions meaningful.

You must be able to create an EXPERIMENT
based on that question
Scientific Inquiry

1. Observing / Come up with a question

2. Asking questions / doing research

3. Forming a hypothesis

Hypothesis = educated guess BASED ON
RESEARCH

4. Testing the hypothesis (Performing the
experiment)
Within the Experiment
INDEPENDENT VARIABLE
 The factor you change on purpose
 Example: The size of the engine. The amount of
fertilizer on plants.
 There can only be ONE
independent variable


DEPENDENT VARIABLE
 The result of what you changed
 Example: The speed of the car. Growth rate of
the plants.
Within the Experiment

CONSTANTS

Factors (variables) you try to keep the same to
make the comparison “fair”
 Example: Test the speed of the car on the
same track with the same car. Same
amount of water & light for the plants.
Within the
Experiment


CONTROL GROUP
 An experiment where one group receives no
treatment. This group is used for comparison.
 Example: Speed of a car that did not get a
larger engine. Growth rate of a plant that did
not get any fertilizer.
EXPERIMENTAL GROUP
 The group that has had the independent
variable added to it.

Example: The car with the bigger engine. Growth rate
of a plant that did receive fertilizer.
Within the Experiment

Scientists ALWAYS confirm results

REPEATED TRIALS
 Repeat the experiment to increase
confidence in your results.
 Average the results to reduce
random error.


Take outliers into account.
More Data = Better Results!

5. Gathering data

More Data = Better Results!
Evidence / Data
Your DATA is evidence
 Evidence is what you observe NOT what you
think is happening.
 Evidence can be:

Measured
 Observed using one’s
senses


But you have to be observant!
Data


QUANTITATIVE DATA
 Results that can be measured and described
with numbers.
 Example: growth rate, speed, length, height,
mass, volume
QUALITATIVE DATA
 Results that are described in words. Results of
our five senses.
 Example: color, texture, “looks healthier”,
“feels softer”, “smells burnt”

6. Conclusion

Restate your hypothesis, and state whether your
data supported or rejected the hypothesis

7. Sharing what has been learned
Communicate your data with colleagues
 Publishing in journals

Science is always tested

Once a scientific idea becomes widely
accepted, it will CONTINUE to be tested and
experimented on.

Every time an experiment is run, new
information is learned
Scientific Notation
Scientific Notation is used to express the very large
and the very small numbers so that problem solving
will be made easier.
Examples:
The mass of one gold atom is
.000 000 000 000 000 000 000 327 grams.
One gram of hydrogen contains
602 000 000 000 000 000 000 000 hydrogen atoms.
Scientists can work with very large and
very small numbers more easily if the
numbers are written in scientific
notation.
How to Use Scientific Notation
• In scientific notation, a number is written
as the product of two numbers…..
…..a coefficient
and 10 raised to
a power.
4.5 x 103
The number 4,500 is written in scientific notation as ________________.
The coefficient is _________.
4.5
The coefficient must be a number greater than or
equal to 1 and smaller than 10.
The power of 10 or exponent in this example is ______.
3
The exponent indicates how many times the coefficient must
be multiplied by 10 to equal the original number of 4,500.
If a number is greater than
10, the exponent will be
positive
_____________
and is equal
to the number of places the
decimal must be moved to
left
the ________
to write the
number in scientific
notation.
If a number is less than 10,
the exponent will be
negative
_____________
and is equal
to the number of places the
decimal must be moved to
right
the ________
to write the
number in scientific
notation.
A number will have an
exponent of zero if:
….the number is equal
to or greater than 1,
but less than 10.
To write a number in scientific notation:
1. Move the decimal to the right of the
first non-zero number.
2. Count how many places the decimal
had to be moved.
3. If the decimal had to be moved to the right,
the exponent is negative.
4. If the decimal had to be moved to the left,
the exponent is positive.
Practice Problems
Put these numbers in scientific notation.
PROBLEMS
1) .00012
2) 1000
3) 0.01
4) 12
5) .987
6) 596
7) .000 000 7
8) 1,000,000
9) .001257
10) 987,653,000,000
11) 8
ANSWERS
1) 1.2 x 10-4
2) 1 x 103
3) 1 x 10-2
4) 1.2 x 101
5) 9.87 x 10-1
6) 5.96 x 102
7) 7.0 x 10-7
8) 1.0 x 106
9) 1.26 x 10-3
10) 9.88 x 1011
11) 8 x 100
EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
1) 4.9 X 102
1) 490
2) 3.75 X 10-2
2) .0375
3) 5.95 X 10-4
3) .000595
4) 9.46 X 103
4) 9460
5) 3.87 X 101
5) 38.7
6) 7.10 X 100
6) 7.10
7) 8.2 X 10-5
7) .000082
Using Scientific
Notation in
Multiplication,
Division, Addition
and Subtraction
Scientists must be able
to use very large and
very small numbers in
mathematical
calculations. As a
student in this class,
you will have to be
able to multiply, divide,
add and subtract
numbers that are
written in scientific
notation. Here are the
rules.
Multiplication
When multiplying numbers written in scientific
notation…..multiply the first factors and add the
exponents.
Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
Solution: Multiply 3.2 x 2.1.
Add the exponents -3 + 5
Answer: 6.7 x 102
Division
Divide the numerator by the denominator. Subtract
the exponent in the denominator from the exponent in
the numerator.
Sample Problem: Divide (6.4 x 106) by (1.7 x 102)
Solution: Divide 6.4 by 1.7.
Subtract the exponents 6 - 2
Answer: 3.8 x 104
Addition and Subtraction
To add or subtract numbers written in scientific
notation, you must….express them with the same
power of ten.
Sample Problem: Add (5.8 x 103) and (2.16 x 104)
Solution: Since the two numbers are not expressed as the same
power of ten, one of the numbers will have to be rewritten in the
same power of ten as the other.
5.8 x 103 = .58 x 104
so .58 x 104 + 2.16 x 104 =?
Answer: 2.74 x 104