•Measurement is the process
of assigning numbers to
quantities. It involves a
quantity and a unit.
Measurement
You are making a measurement when you
Check you weight
Read your watch
Take your temperature
Weigh a watermelon
What kinds of measurements did you
make today?
Where did it come from?
Why 12 inches?
The King’s Foot
One Foot
The King’s Foot
One Foot
Too big for some things...
...So they used the length of the
King’s first knuckle
One Inch
Why 12 inches not 10 or 13?
Simply because it took 12 lengths of
his first knuckle to equal his foot.
...So they used the length of the
King’s first knuckle
One Inch
But that was too big for some other
things...
...That’s exactly how they made
inches. the fractions between the
1/2
1/4
...So they cut the inches into
fractions
1/2
1/4
1/8
and 1/16
You should have noticed that
as the fractions got smaller,
so did the length of the lines
between the whole numbers.
That helps to identify a half
from the fourths and so on.
If you don’t remember what
the fraction is just by looking
at the ruler, you can always
count the number of lines
between the whole numbers.
If there are 16, then your
ruler is divided into
sixteenths.
..then you can do the math to
determine the fraction.
If you counted 10 lines from the whole number, that
would be 10 sixteenths. Here’s where that “magic
number 2” comes in.
To get the fraction to it’s lowest possible denominator
DIVIDE both numbers in the fraction by 2 and keep
doing it until the top number is odd.
10 = 5
Top number’s odd so 10/16 = 5/8
16 8
If the fraction comes between two whole numbers
like 1 and 2, then the measurement is the first whole
number and the fraction in this case it would be 1
and 5/8ths
A.
B.
C.
D.
Name this measurement
A. 1/2
B. 1/3
C. 1/4
D. 5/16
Name this measurement
A.
B.
C.
D.
A. 3/4
B. 3/8
C. 1-3/4
D. 2-3/4
The Metric ruler is much
different. Everything is based on
10
10mm (millimeters) = 1cm (centimeter)
100cm= 1m (meter)
1m = 100cm (cm = centimeter, cent
means 100)
1m = 1000mm (mm = millimeter, mil means
1000)
The Metric Ruler
This is a magnified
image of a ruler/meter
stick.
1
2
3
4
This is half of a centimeter.
This is a magnified
image of a ruler/meter
stick.
1
2
3
4
This is one millimeter.
TWO SYSTEMS OF
MEASUREMENT
ENGLISH
SYSTEM
English Base Units
• For measuring length a yard is used
and one yard = 0.914 meters
• An inch is used for measuring the
length of smaller objects and 1inch =
2.54 cm
English Base Units
• For measuring mass the pound is
used and one pound = 0.45
kilograms
English Base Units
• An ounce is used for measuring the
mass of smaller objects and 1 ounce
= 28.35 grams.
English Base Units
• For measuring volume a gallon is
used and 1 gallon = 3.78 liters
English Base Units
• A fluid ounce (oz.) is used to
measure the volume of smaller
objects and 1 fluid ounce = 29.6
milliliters
Metric
System
Metric System
• The metric system is based on a base unit
that corresponds to a certain kind of
measurement
• Length = meter
• Volume = liter
• Weight (Mass) = gram
• Prefixes plus base units make up the
metric system
– Example:
• Centi + meter = Centimeter
• Kilo + liter = Kiloliter
Metric System
• The three prefixes that we will use
the most are:
– kilo
– centi
– milli
Base Units
kilo
hecto
deca
meter
gram
liter
deci
centi
milli
Metric System
• So if you needed to measure length
you would choose meter as your
base unit
– Length of a tree branch
• 1.5 meters
– Length of a room
• 5 meters
– Length of a ball of twine stretched out
• 25 meters
Metric System
• But what if you need to measure a
longer distance, like from your house
to school?
– Let’s say you live approximately 10 miles
from school
• 10 miles = 16093 meters
– 16093 is a big number, but what if you
could add a prefix onto the base unit to
make it easier to manage:
• 16093 meters = 16.093 kilometers (or 16.1 if
rounded to 1 decimal place)
Metric System
• These prefixes are based on powers of 10.
What does this mean?
– From each prefix every “step” is either:
• 10 times larger
or
• 10 times smaller
– For example
• Centimeters are 10 times larger than millimeters
• 1 centimeter = 10 millimeters
Base Units
kilo
hecto
deca
meter
gram
liter
deci
centi
milli
Metric System
– Centimeters are 10 times
larger than millimeters so it
takes more millimeters for the
same length
1 centimeter = 10 millimeters
Example not to scale
40
1 mm
41
1 mm
1 mm
1 mm
1 mm
1 mm
40
1 mm
1 mm
1 mm
1 mm
41
1 cm
Metric System
• For each “step” to right,
you are multiplying by 10
• For example, let’s go from a base unit to centi
1 liter = 10 deciliters = 100 centiliters
( 1 x 10 = 10)
=
(10 x 10 = 100)
2 grams = 20 decigrams = 200 centigrams
(2 x 10 = 20)
kilo
hecto
deca
meter
liter
gram
=
(20 x 10 = 200)
deci
centi
milli
Metric System
• An easy way to move within the metric
system is by moving the decimal point one
place for each “step” desired
Example: change meters to centimeters
1 meter = 10 decimeters = 100 centimeters
or
1.00 meter = 10.0 decimeters = 100. centimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Now let’s try our previous example from
meters to kilometers:
16093 meters = 1609.3 decameters = 160.93
hectometers = 16.093 kilometers
• So for every “step” from the base unit to kilo,
we moved the decimal 1 place to the left
(the same direction as in the diagram below)
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• If you move to the left in the diagram,
move the decimal to the left
• If you move to the right in the diagram,
move the decimal to the right
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Now let’s start from centimeters and convert
to kilometers
400000 centimeters = 4 kilometers
400000 centimeters = 4.00000 kilometers
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Now let’s start from meters and convert to kilometers
4000 meters = 4 kilometers
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
• Now let’s start from centimeters and convert to
meters
4000 centimeters = 40 meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Now let’s start from meters and convert to centimeters
5 meters = 500 centimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
• Now let’s start from kilometers and convert to meters
.3 kilometers = 300 meters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Now let’s start from kilometers and convert to
millimeters
4 kilometers = 4000000 millimeters
or
4 kilometers = 40 hectometers = 400 decameters
= 4000 meters = 40000 decimeters
= 400000 centimeters = 4000000 millimeters
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Metric System
• Summary
– Base units in the metric system are meter, liter,
gram
– Metric system is based on powers of 10
– For conversions within the metric system, each
“step” is 1 decimal place to the right or left
– Using the diagram below, converting to the right,
moves the decimal to the right and vice versa
kilo
hecto
deca
meter
liter
gram
deci
centi
milli
Systems of Measurement
• Why do we need a standardized system of
measurement?
– Scientific community is global.
– An international “language” of measurement
allows scientists to share, interpret, and compare
experimental findings with other scientists,
regardless of nationality or language barriers.
• By the 1700s, every country used its own
system of weights and measures. England
had three different systems just within its own
borders!
Metric System & SI
• The first standardized system of
measurement: the “Metric” system
– Developed in France in 1791
– Named based on French word for “measure”
– based on the decimal (powers of 10)
• Systeme International d'Unites
(International System of Units)
– Modernized version of the Metric System
– Abbreviated by the letters SI.
– Established in 1960, at the 11th General
Conference on Weights and Measures.
– Units, definitions, and symbols were revised and
simplified.
UNIT CONVERSIONS
• Quantities can be converted from one
type of unit to another. This conversion
may occur within the same system
(metric or English) or between systems
(metric to English or English to metric).
• Conversions cannot be made between
measures of different properties, that is,
mass units to length units for example.
• A method of unit conversion commonly
used is called Dimensional Analysis or Unit
Analysis. In this procedure, units are used
to decide when to multiply or divide in
order to obtain the correct answer.
FROM THE CONVERSION TABLE
CANCEL UNITS TO LEAVE UNITS OF THE ANSWER
Perform the operations
Dimensional/ Unit Analysis – metric to
metric
1. How many meters are contained in 800cm?
800 cm  m
800 cm x 1 m
100 cm
= 800
100
=8m
2. How many Kg are there in 1200 g?
1200g  Kg
1200 g x 1Kg
1000 g
= 1200
1000
= 1.2 Kg
Dimensional/Unit Analysis – English 
metric
1. How many grams are contained in 25 lbs?
25 lbs  g
25 lbs x 1Kg
x 1000g = 25 000
2.2 lbs
1 Kg
2.2
=11 363.63 g
2. How many pounds are there in 75 Kg?
75Kg  lbs
75 Kg x 2.2 lbs = 165 lbs
1 Kg
* How many seconds are there in
90 minutes?
90 mins  secs
90 mins x 60 secs = 5400 secs
1 min
* How many minutes are there in
2 days and 6 hours?
2 days, 6 hrs  mins
2 days x 24 hrs = 48 hrs + 6 hrs = 54 hrs
1 day
54 hrs x 60 mins = 3 240 mins
1 hr
Convert the following using
Dimensional Analysis
• 1) 950 g  Kg
• 2) 112 lbs  g
• 3) 25 L  ml
• 4) 3.5Km  m
• 5) 2 days & 3 hours  min