Metric System Basics
(with credit to Mr. Paves and the sites at pulse.pharmacy.arizona.edu/math/lesson_gifs/how_big/metrics.ppt,
http://www.beverlyschools.org/memorial/di/Math/metricsystem/metricsystem.pdf and www.sciencespot.net/Media/metric_metconv.ppt)
What is the Metric System?
• The first standardized system of measurement, based on
the decimal was proposed in France about 1670.
• However, it was not until 1791 that such a system was
developed.
• It was called the "metric" system, based on the French
word for measure.
• At that time, every country had their own system of
weights and measures. England had three different
systems just within its own borders!!
• On May 20, 1875, delegates of 17 countries signed the
Meter Convention. It was amended in 1921 and today
every country in the world has adopted the Metric
System accept for Liberia, Myanmar and the U.S.A.
Why Do We Use The Metric System?
• Almost all other countries are using the metric
system
• Other countries’ companies are refusing to
buy products from the U.S. if not labeled in
metric units
• Scientists need a universal way to
communicate data (SI Units)
Metric System
• The metric system is based on a base unit that
corresponds to a certain kind of measurement
• Length = meter (m)
• Volume = liter (L)
• Weight (Mass) = gram (g)
• Prefixes plus base units make up the metric
system
– Example:
• Centi + meter = Centimeter (cm)
• Kilo + liter = Kiloliter (kL)
Metric System
• The three prefixes that we will use the most
are:
– Kilo- (k_)
– Centi- (c_)
– Milli- (m_)
Base Units
kilo
(km, kg or
kL)
hecto
(hm, hg, hL)
deca
(dam, dag,
daL)
Meter (m)
gram (g)
Liter (L)
deci
(dm, dg, dL)
centi
(cm, cg,
cL)
milli
(mm, mg,
mL)
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)
Measurement Conversions to Know:
•
•
•
•
•
•
•
•
1 m = 100 cm
1 cm = 10 mm
1 m = 1,000 mm
1 km = 1,000 m
1 g = 100 cg
1 cg = 10 mg
1 g = 1,000 mg
1 kg = 1,000 g
1 L = 100 cL
1 cL = 10 mL
1 L = 1,000 mL
1 kL = 1,000 mL
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
What is the order of the metric
system?
• King Henry Died by Drinking Chocolate Milk
– King: Kilo
– Henry: Hecto
– Died: Deca
– By: Base (m, L, g)
– Drinking: Deci
– Chocolate: Centi
– Milk: 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
Converting Units:
THE Golden Rule
• When going from a
big unit to a small
unit:
• MULTIPLY!!
• Or move decimal
place to the right;
add zeros as needed
as place holders.
• When going from a
small unit to a big
unit:
• DIVIDE!!
• Or move decimal
place to the left; add
zeros as needed as
place holders.
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
Practice
• Try these conversions and in your notes
1000 mg = _______ g
1 L = _______ mL
14 km = _______ m
109 g = _______ kg
160 cm = _______ mm
250 m = _______ km
• Compare using <, >, or =.
56 cm
6m
7g
698 mg
Assignment
Write the correct abbreviation for each metric unit.
1) Kilogram _____
4) Milliliter _____
7) Kilometer _____
2) Meter _____
5) Millimeter _____
8) Centimeter _____
3) Gram _____
6) Liter _____
9) Milligram _____
10) 2000 mg = _______ g
15) 5 L = _______ mL
20) 16 cm = _______ mm
11) 104 km = _______ m
16) 198 g = _______ kg
21) 2500 m = _______ km
12) 480 cm = _____ m
17) 75 mL = _____ L
22) 65 g = _____ mg
13) 5.6 kg = _____ g
18) 50 cm = _____ m
23) 6.3 cm = _____ mm
14) 8 mm = _____ cm
19) 5.6 m = _____ cm
24) 120 mg = _____ g
Try these conversions.
Assignment (cont.)
Compare using <, >, or =.
25) 63 cm
26) 536 cm
6m
53.6 dm
27) 5 g
28) 43 mg
508 mg
5g
29) 1,500 mL
30) 3.6 m
1.5 L
36 cm