MEASUREMENT
Units of Measurement : SI unit and derived units
Unit prefixes
Unit conversion using dimensional analysis
Scientific notation
Increment, Accuracy, Precision
OBJECTIVES
Distinguish between a number and a quantity.
Name SI units for length, mass, time, temperature,
volume and density.
Define and identify base units; unit conversions;
identify prefixes
Perform unit conversion using dimensional analysis.
Units of Measurement
•In our daily lives we deal with making
measurements routinely.
–i.e., How much gasoline is required to fill your gas tank? What
time did you wake up this morning? How fast did you drive to
school today ?
•Doctors, nurses, pharmacists–Doctors and nurses make measurements constantly.
Measurements like pulse rate, blood pressure, temperature,
drug dosage.
•Math - The language of Science
–Scientists make countless measurements during their
experiments to prove or disprove a theory.
Units of Measurement
What is your response if I told you that:
I weigh 65
In any measurement
magnitude (the number) as
well as the unit (meaning)
must be stated.
Otherwise, it is meaningless!
Number vs. Quantity
• Quantity : number + unit
UNITS MATTER!!
Systems of Measurement
What units are used?
The Rest of the
World
America
English System
1 ft = 12 in
1 yd= 3 ft
1 mi. = 1,760 Yd
1 mi = 5280 ft
Metric System
1 km = 1000 m
1 m = 100 cm
Scientific
Community
Le System
International d’Unites
SI Units are basically an
updated form of the
metric system.
Metric system and the
Le Systeme International d'Unites (SI)
• The Metric system is convenient because it uses only
one fundamental unit for each type of measurement.
For example for:
*Length we use only meter, in the US we use foot,
yard, inch.
*Mass we use Kg not pound.
• All the Prefixes are multiples of 10.
SI Units
Quantity
Symbol
Base Unit
Abbrev.
Length
l
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temp
T
kelvin
K
n
mole
mol
Amount of particles
SI Prefix Conversions
Prefix
Giga
Symbol
G
Factor
109
k
h
da
---
106
103
102
10
1
deci-
d
10-1
centi-
?
milli-
m
10-3
micro-

10-6
MegakiloHectoDekaBASE UNIT
Derived Units: Combination of base units
• Area ( m2)
• length  length = m x m
• Volume (m3)
– length  length  length= m x m x m
• Density (g/cm3)
– mass per volume
M
D=
V
Temperature
A measure of how hot or how cold an
object is.
SI Unit: the kelvin
• Note: not a degree
• Absolute Zero= 0 K
(K)
Temperature Scales
Celsius and Kelvin
K= oC + 273
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 = 11,200 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 = 29 mL
Unit 1 - MEASUREMENT
Unit conversion using dimensional
analysis
Page
SI Prefix Conversions
1. Find the difference between the
exponents of the two prefixes.
2. Move the decimal that many places.
To the left
or right?
move right
move left
SI Prefix Conversions
Prefix
Symbol
Giga
G
MegakiloHectoDecaBASE UNIT
Factor
109
106
k
H
D
---
103
102
10
1
deci-
d
10-1
centi-
?
milli-
m
10-3
micro-

10-6
SI Prefix Conversions
1) 20 cm =
___________ m
2) 0.032 L =
______________ mL
3) 45 m =
______________ cm
4) 80.5 km =
______________ m
How would you convert 2h 45
min to second
Convert 55.00 km/h to m/s
Converting by using Dimensional
Analysis
•
Steps:
1. Identify starting ( also called given, old )&
ending ( target, new) units.
2. Line up conversion factors so units cancel.( hint :
the new units should on the top)
3. Multiply all top numbers & divide by each bottom
number. ( )
4. Check units & answer.
Converting by using Dimensional
Analysis: inch to cm
Identify
10.0 in
We start by writing down the
Given (old) and its Unit
Converting by using Dimensional
Analysis: inch to cm
Line up
10.0 in x 2.54 cm
1 in
We know 1 in = 2.54 cm. So our conversion
factor is : 1 in = 2.54 cm. Since we want to
convert to cm, it goes on the top. ( Hint)
Converting by using Dimensional
Analysis: inch to cm
Cancel units
2.54
cm
10.0 in x
1 in
Now we cancel and collect units. The inches cancel
out, leaving us with cm : the Target unit.
Converting by using Dimensional
Analysis: inch to cm
10.0 in x 2.54 cm = 25.4 cm
1 in
Since the unit is correct,
all is left to do the math ...
The
Answer
Lets check it out !!!!!!
Find the 10 in mark and directly across
at the cm side. What number do you find?
Converting by using Dimensional
Analysis: inch to cm
5) You go to Europe and decide to have a haircut. Your
hairdresser wants to cut your hair 8.0 cm shorter. How
many inches will he be cutting off?
Identify , line up, cancel out, multiply, check
8.0 cm
1 in
2.54 cm
= ? in
Question: Is the conversion Factor the same?
What’s the difference?
Converting by using Dimensional
Analysis: g to Kg
• Convert 250 g into Kg
Identify , line up, cancel out, multiply, check
250 g x 1Kg
1000 g
=
Kg
Converting by using Dimensional
Analysis: Kg to g
• Convert 1.5 Kg into g
• Identify : Given and Target unit
• Line up: Conversion Factor
1.5 kg x
=
g
Q: Which conversion factor will you be using?
1Kg = 1000g or 1000g= 1Kg
A more complex conversion
km to m
hr
s
kilometers into meters and hour into second.
We can do both conversions at once using
the same method as in the previous
conversion.
A more complex conversion
km to m
Identify
80 km
hr
hr
s
Write down the
_____and ____
A more complex conversion
km to m
hr
s
Line up
1
hr
80 km x
hr 3600 s
First conversion factor is: 1 hour = 3600 sec.
A more complex conversion
km to m
Line up
hr
s
80 km x 1 hr x 1000 m
hr
3600 s 1 km
The second conversion factor is: 1 km = 1000 m.
A more complex conversion
km
to
m
Cancel out units
hr
s
80 km x
1 hr x 1000 m
hr 3600 s 1 km
m
=
s
Check your units !!!
If you have chosen the correct conversion factors, you
should only be left with the units you want to convert to.
A more complex conversion
km to m
hr
s
80 km x 1 hr x1000 m
=
hr 3600 s 1 km
80,000 m
=
3600 s
m
s
The
Answer!!
A Very more complex conversion
to finish at home today !!
Problem1:Convert 1 year into seconds
year
seconds
1y
=
1y
365 days
24h
1h
1day
60s
s
Dimensional Analysis
Problem2: Taft football needs 550 cm for a 1st
down. How many yards is this?
cm
yd
550 cm
=
1 yd
1 in
12in
3 ft
2.54 cm
1ft
yd
Dimensional Analysis
Problem3: A piece of wire is 1.3 m long.
How many 1.5-cm pieces can be cut
from this wire?
cm
1.3 m
pieces
=
pieces
Dimensional Analysis
•Problem5:How old are you in
minutes?
Age in y
=
min
Homework
Units and Conversions HW
Due: tomorrow
How would you convert 2h 45
min to second
Convert 55.00 km/h to m/s
Scientific Notation
Mx
n
10
• M is the coefficient 1<M<10
• 10 is the base
• n is the exponent or power of 10
Other Examples:
5.45E+6
5.45 x 10^6
Numbers less than 1 will have a
negative exponent.
Numbers bigger than 1 will have a
positive exponent.
A millionth of a second is:
0.000001 sec
1.0E-6
1.0x10^-6
Limits of Measurement
• Accuracy and Precision
• Accuracy - a measure of how
close a measurement is to the
true value of the quantity being
measured.
Example: Accuracy
• Who is more accurate (Susan or
Amy) when measuring a book that
has a true length of 17.0cm?
Susan:
18.1cm, 16.0cm, 18.0cm, 17.1cm
Amy:
16.5cm, 16.0cm, 16.2cm, 16.3cm
• Precision – a measure of how
close a series of measurements
are to one another. A measure of
how exact a measurement is
regardless is it is close to the real
value.
Example: Precision
Who is more precise when measuring
the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the
following are precise, accurate or
both.
Accurate
Not Accurate Accurate
Not Precise Precise
Precise
Graduated Cylinder - Meniscus