Metric Units and Measurement
Units of Measurement
Why do we need a “standard” unit of Measurement?
– Report Data that can be reproduced
Base Units
– Time = Seconds (s)
– Length = meter (m)
– Mass = kilogram (kg)
– Volume = space occupied by an object
• Liter (L)
Metric Units
Derived Units Continued
Now What are the units for the following?
– Mass = ?
• Grams or g
– Volume = ?
• mL or cm3
Now… Insert them into the formula!
g
D=
mL
or
g
D=
3
cm
Derived Units
= Combination of base units
Example: Density
• Density = Mass Divided by Volume
– How would we write this? Use symbols.
M
D=
V
Now What are the units for the following?
– Mass = ?
• Grams or g
– Volume = ?
• mL or cm3
Density
So… Density is the Ratio of Mass to Volume.
M
D=
V
Determining Volume
• Here is an odd shaped Object…
• How would you find the volume if you
couldn’t take any measurements?
• Water displacement that’s how…
• What happens when you get into a bath tub
that is filled to the top with water?
– That’s right it over flows! Why..
Water displacement
Water Displacement
• Let’s take our object
• And a graduated Cylinder filled with some water
… enough to cover the object
• … but not completely filled (remember what
happened to the bath tub!)
Water Displacement and Volume
• What would happen if we placed our object
… into the graduated cylinder?
• The Water level starts at..
– 46 mL
• Ends at 66 mL
• What’s the difference…
– 20 mL
– That’s the volume of the
object
Using the Density formula answer
the following questions.
• A piece of metal with a mass of 147g is placed in a
50mL graduated cylinder. The water level rises from
20mL to 41mL. What is the density of the metal?
• What is the volume of a sample that has a mass of
20g and a density of 4 g/mL?
Units
• All measurements start with the base unit
– Length is m or meters
– Volume is L or liters
– Mass is g or grams
• How ever… what if the object is less than the base
unit?
• Let’s look at length or meters (m)
1 meter
Units continues
• Each unit (m, L, g) is broken down into parts of 10
• Lets break this meter stick into 10 parts
1 meter
1
2
3
4
5
6
7
• Each part is 1/10th of a meter
• Each part is called a decimeter or dm
• So… what is the length of this nail?
– 4 dm or 4 decimeters
8
9
10
• This is 1 dm
• This is 1 mm
• This is 1 cm
Prefixes Used with SI Units
Examples
Centimeter = ?
– 100th of a meter or .01 or 10-2
Kilometer = ?
– 1000 meters or 10 3
Millimeter
– 1000th of a meter / or .001 / or 10-3
Temperature
What is the SI Unit of Temperature?
– Kelvin (K)
• 273 K = freezing point of water
• 373 K = boiling point of water
What’s the difference between the two?
– 100 degrees
What is Celsius?
– Temperature measurement based on 0o – 100o C
We will always convert Celsius to Kelvin, unless told
not to.
Converting Kelvin to Celsius
Convert - Celsius to Kelvin
–
oC
(what you measured) + 273 K = Kelvin
Convert – Kelvin to Celsius
– oK (what you measured) – 273 K = oCelsius
Convert the following to Kelvin
– 357o C
– -39o C
Convert the following to Celsius
– 266 K
– 332 K
Activity – miniLAB - Density
• Follow the directions on page 15 of your book
• We will be doing a lab write up on this lab.
NEXT CLASS: Chapter 2:1 / 2:2
•Homework: WB 2:1 / 2:2
•Quiz 3: Day 5 (Chapter 2:1 / 2:2)
TODAY: Chapter 2:2 / 2:3
DAY 5
– NO QUIZ!!!
– Density LAB
– Sections 2 AND 3
– Next Class Sections 2 AND 3
– HW: Sections 2 and 3
Homework:
– Homework: WB 2:2 / 2:3
• Quiz 3: Day 6 (Chapter 2:2 / 2:3)
Density Lab
• Materials;
– Cork stopper, Rubber stopper, Nut and bolt
– Graduated cylinder, water
Formula:
D=M/V
Data Table:
MASS
VOLUME
Final (mL)
Cork Stopper
Rubber Stopper
Nut & Bolt
Initial (mL)
DENSITY
Volume
Convert to Scientific Notation
Pretest
• 134,000
• 5,400
• 0.001034
• 0.00078
Scientific Notation
What's the goal of Scientific Notation?
– Condense the number that is written
Example: What would you rather write
– 0.00000000000000000456
Or
– 4.56 x 10-18
Rules of Scientific Notation
• It’s all about the decimal point! And power of 10!
Example: 645,000
1st… move the decimal point so one # is to the left
of it
6.45000
2nd… place “x 10” to the right
6.45000 x 10
3rd… count the number of spaces you moved the
decimal point.
6.45000 X 105
Almost Done!
• 6.45000 X 105
Now get rid of the zeros
6.45 X 105
Rules:
#1..moving the decimal point to the left…
the exponent gets bigger
#2… moving the decimal point to the right…
the exponent gets smaller
64.5 X 10… what's the exponent
6.45 X 104
Adding Exponents
Rules:
1st… exponents need to be the same. Move the
decimal point until the two numbers have the
same exponent
2nd… add OR subtract the numbers… not the
exponents.
Example: Add the following #s…Follow the Rules
6.45 x 105
3.11 x 104
Answer: 6.76 x 105
Practice problems pg 32
Addition and Subtraction
•Every problem
Pretest
• Multiply (2 x 103) x (3 x 102)
• Divide (9 x 108) ÷ (3 x 10-4)
Multiplying / Dividing
Multiplying
Rules:
– 1st… multiply the numbers
– 2nd… add the exponents
Dividing
Rules
– 1st… divide the numbers
– 2nd… subtract the exponents
Practice Problems pg 33
Multiply
(2 x 103) x (3 x 102) =
Divide
(9 x 108) ÷ (3 x 10-4) =
Rules:
Conversions
1st… write down what you know
2nd… write down what you want to know
3rd… what conversion factor are you going to use to
get there?
Convert 48km to meters (factor: 1km=1000meters)
1000𝑚
1𝑘𝑚
48𝑘𝑚
1
or
1𝑘𝑚
1000𝑚
1000𝑚
1𝑘𝑚
=______m
48000
Types of Measurements
• Precise vs. Accurate
Percent Error
• The Accepted value is a known value
• Error = Accepted - Measured
% error example
• The accepted density for copper is 8.96g/mL.
Calculate the percent error for each of these
measurements.
1.11%
• 8.86 g/mL
.45%
• 8.92 g/mL
• 9.00 g/mL
.45%
• 8.98 g/mL
.22%
Significant Figures or Sig Figs
Tells the how precise the measurement is
• Example: Which is more precise?
3.5 or 3.52g
Rules for Sig Figs – pg. 39
1. Non-zero umbers are always significant
2. Zeros between non-zero numbers are always
significant
3. All final zeros to the right of the decimal place are
significant.
4. Zeros that act as placeholders are NOT significant.
Convert quantities to scientific notation to remove
the placeholders.
5. Counting numbers and defined constants have an
infinite number of significant figures.
Examples – use your rules
• Which numbers are significant?
 72.3
60.5
6.20
0.0253
4320
125000
• Help yourself out – convert to Scientific Notation
Rounding Numbers – pg 40
1. If the digit to the immediate right of the last sig fig is
less than five, do not change the last sig fig.
2. If the digit to the immediate right of the last sig fig is
greater than five, round up the last sig fig
3. If the digit to the immediate right of the last sig fig is
equal to five and is followed by a nonzero digit, round
up the last sig fig.
4. If the digit to the immediate right of the last sig fig is
equal to five and is not followed by a nonzero digit,
look at the last sig fig. if it is an odd digit, round it up.
If it is an even digit, do not round up