1. The Wonderful World of
Metrics!

2. way of measuring things. The practice is the same, but different
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?

3. The “Basics” foundation. Those units are…..
 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

4. units. But how is that possible…
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…

5. Pioneering the Prefixes
 Lets start with the prefixes for large measurements….
 KILO (k) kilometer = 1000 meters
 HECTO (h) Hectoliter = 100 liters
 DECA (da) Decagram = 10 grams
 Remember Meters, Liters, Grams, and Seconds are
the base units. They will be in every measurement.

6. r way to Pioneering the Prefixes base root word remember all this?
 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 easier way
remember all this?
r way to

7. Can you Think of your own?
Good ol’ King Henry
King Henry Died by Drinking Chocolate Milk
Kilo
Hecto
Deca
Base
Deci
Centi
Milli
Can you Think of your own?

8. Converting Skillz unit move the decimal to the left.
 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.

9. K h da b d c m 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.

10. K h da b d c m 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.

11. K h da b d c m Practice makes Perfect! Last one!
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.

12. Precision vs Accuracy  Precision  Accuracy
 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?

13. Precision vs Accuracy

14. Density

15. 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

16. Density in an object. volume.
 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.

17. The Math…  The Units:  Mass = Grams (g)  Volume (2 ways)
 Ruler = cm3
 Displacement = ml
 Density (2 ways)
 Ruler = g/cm3
 Displacement = g/ml

18. Wood Water Iron What is Density?
If you take the same volume of different substances, then
they will weigh different amounts.
Wood Water Iron
0.50 g g g
Q) Which of these is most dense? Why?
cm3
cm3
cm3
IRON! It has the most mass for that volume.

19. of 1 g/cm3 Density for different things… own density.
Substance Density (g/cm3)
 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
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
(This is the only density you need to memorize!)
Lead

20. Density for different things…
Substance
Density
 Objects with different densities
interact in a very predictable way
 The more dense object will sink, the
less dense will rise to the top… 3
(g/cm )
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

21. 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)

22. Sidenote…
Sulfur hexaflouride. Density? Explain this.

23. The Math…  The Units:  Mass = Grams (g)  Volume (2 ways)
 Ruler = cm3
 Displacement = ml
 Density (2 ways)
 Ruler = g/cm3
 Displacement = g/ml

24. Find the mass of the object
Determining Density
Step 1:
Find the mass of the object

25. 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

26. Determining Density Step 3: Calculate Density = Mass Volume Units:
For ruler: g/cm3
For displacement: g/ml

27. space, calculate the 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:

28. 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 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 Unknown: Density (g/cm3) Volume = 7 cm3
Formula: D = M / V Solution: D = 35g / 7cm3
D = 5g/cm3
To find density:
. If the mass of an

29. Practice Problem 1 Osmium is a very dense metal. What is its
density in g/cm3 if g of the metal occupies
a volume of 2.22cm3?
1) g/cm3
2) g/cm3
3) g/cm3

30. 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/ cm B) 6 g/cm C) 252 g/cm3
25 ml mL
lecturePLUS Timberlake

31. The
Nature of
Science
(How Scientists Think)

32. Why Science? natural world we live in.
 The goal of science is to understand the
natural world we live in.

33. Why Hypothesize? explain what they think will happen in a certain
 Scientist hypothesize in order to try to
explain what they
think
will
happen in a
certain
situation
Long-held assumptions
should be questioned!

34. How do you achieve Scientific success?
 Be creative: think outside the box!
 Those “Creative” experiments end up being
the best ones.

35.  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.

36. questions meaningful. based on that question
 Question everything, but make your
questions meaningful.
 You must be able to create an EXPERIMENT
based on that question

37. Scientific
Inquiry
 1. Observing / Come up with a question

38.  2. Asking questions / doing research

39.  3. Forming a hypothesis
 Hypothesis = educated guess BASED ON RESEARCH

40.  4. Testing the hypothesis (Performing the
experiment)

41. Within the Experiment fertilizer on plants. independent variable the
 The factor you change on purpose
 Example: The size of
fertilizer on plants.
 There can only be ONE
independent variable
the
engine.
The
amount of
 DEPENDENT VARIABLE
 The result of what you
changed
 Example: The speed of the car.
the plants.
Growth rate of

42. Within the Experiment to make the comparison “fair”  CONSTANTS
 Factors (variables) you try to keep the same
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. to

43. Within the Experiment group receives no treatment.
 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.

44.  Take outliers into account.
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!

45.  5. Gathering data
 More Data = Better Results!

46. Evidence / Data think is happening. observe NOT what you senses
 Your DATA is evidence
 Evidence is what you
think is happening.
 Evidence can be:
 Measured
 Observed using one’s
senses
observe
NOT
what
you
 But you have to be observant!

47. Data measured and described with numbers. rate, speed, length, height,
 QUANTITATIVE DATA
 Results that can be
with numbers.
 Example: growth mass, volume
 QUALITATIVE DATA
measured and described
rate, speed, length, height,
 Results that are described
our five senses.
 Example: color, texture,
in words. Results of
“looks healthier”,
“feels softer”, “smells burnt”

48.  6. Conclusion
 Restate your hypothesis, and state whether your data supported or rejected the hypothesis

49.  7. Sharing what has been learned
 Communicate your data with colleagues
 Publishing in journals

50. Science is always tested accepted, it will CONTINUE to be tested
 Once a scientific idea becomes widely
accepted, it will CONTINUE to be tested
experimented on.
 Every time an experiment is run, new information is learned
and

51. Scientific Notation

52. The mass of one gold atom is .000 000 000 000 000 000 000 327 grams.
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
grams.
One gram of hydrogen contains
hydrogen atoms.
Scientists can work with very large and very small numbers more easily if the numbers are written in scientific notation.

53. 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.

54. For example: 4.5 x 103 The coefficient is _________. 4.5
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.

55. Rules to Remember!
If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
positive
left

56. Rules to Remember!
If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
negative
right

57. A number will have an exponent of zero if:
….the number is equal to or greater than 1, but less than 10.

58. 1. Move the decimal to the right of the first non-zero number.
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.

59. ANSWERS PROBLEMS 1.2 x 10-4 1 x 103 1 x 10-2 1.2 x 101 9.87 x 10-1
Practice Problems
Put these numbers in scientific notation.
PROBLEMS
1.2 x 10-4
1 x 103
1 x 10-2
1.2 x 101
9.87 x 10-1
5.96 x 102
7.0 x 10-7
1.0 x 106
1.26 x 10-3
9.88 x 1011
8 x 100
ANSWERS
.00012
1000
0.01 12
.987
596
1,000,000
987,653,000,000 8

60. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS
PROBLEMS
ANSWERS
4.9 X 102
3.75 X 10-2
5.95 X 10-4
9.46 X 103
3.87 X 101
7.10 X 100
8.2 X 10-5
490
.0375
9460
38.7
7.10

61. 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.

62. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)
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 Add the exponents
Answer: 6.7 x 102

63. Sample Problem: Divide (6.4 x 106) by (1.7 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 Subtract the exponents 6 - 2
Answer: 3.8 x 104

64. 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 so .58 x x 104 =?
Answer: x 104