Transcript 20 METRIC SYSTEM

The METRIC SYSTEM
& CONVERSIONS
MSJC ~ San Jacinto Campus
Math Center Workshop Series
Janice Levasseur
The Metric System
• The metric system is an internationally
standardized system of units of
measurement.
• The metric system is based on a base
unit and prefixes.
Prefixes
•
•
•
•
•
•
•
Kilo Hecto Deca Deci Centi Milli -
1000
100
10
1
0.1
0.01
0.001
k
h
da
d
c
m
Length
• The basic unit of length in the metric system is
the meter (m)
• Metric Units of Length
–
–
–
–
–
–
–
Kilometer (km) = 1000 m
Hectometer (hm) = 100 m
Decameter (dam) = 10 m
Meter (m) = 1 m
Decimeter (dm) = 0.1 m
Centimeter (cm) = 0.01 m
Millimeter (mm) = 0.001 m
Mass
• Weight is a measure of how strongly
gravity is pulling on an object (decreases
as elevation increases)
• Mass is the amount of material in an
object (doesn’t change)
• Note: on Earth, weight and mass are
used interchangeably
Mass
• The basic unit of mass in the metric system is a
gram (g)
• 1 g = mass of water in a cube that measures 1
cm x 1 cm x 1cm
• Metric Units of Mass
–
–
–
–
–
–
–
Kilogram (kg) = 1000 g
Hectogram (hg) = 100 g
Decagram (dag) = 10 g
Gram (g) = 1 g
Decigram (dg) = 0.1 g
Centigram (cg) = 0.01 g
Milligram (mg) = 0.001 g
Capacity
• Liquid substances are measured in units of capacity.
• The basic unit of mass in the metric system is a liter (L)
• 1 L = capacity of a cube that measures 10 cm x 10 cm
x 10 cm
• Metric Units of Capacity
–
–
–
–
–
–
–
Kiloliter (kL) = 1000 L
Hectoliter (hL) = 100 L
Decaliter (daL) = 10 L
Liter (L) = 1 L
Deciliter (dL) = 0.1 L
Centiliter (cL) = 0.01 L
Milliliter (mL) = 0.001 L
Conversions within the Metric
System
• To convert units within the metric system,
write the prefixes in order from largest to
smallest
k
h
da
d
c
m
• To convert from a smaller unit to a larger unit,
move to the left
• To convert from a larger unit to a smaller unit,
move to the right
Ex: Convert 1600 cm to m
• km
hm
dam
m
dm
cm
mm
• Move 2 places to the left to get from cm to m
• Therefore, move the decimal point in 1600
two places to the left to convert from cm to m
 1600 cm = 16.00 m
Ex: Convert 2 kL to L
• kL
hL
daL
L
dL
cL
mL
• Move 3 places to the right to get from kL to L
• Therefore, move the decimal point in 2 three
places to the right to convert from kL to L
 2 KL = 2000 L
Ex: Convert 241 g to mg
• kg
hg
dag
g
dg
cg
mg
• Move 3 places to the right to get from g to mg
• Therefore, move the decimal point in 241 three
places to the right to convert from g to mg
 241 g = 241,000 mg
Ex: Convert 3 mL to L
• kL
hL
daL
L
dL
cL
mL
• Move 3 places to the left to get from mL to L
• Therefore, move the decimal point in 3 three
places to the left to convert from mL to L
 3 mL = 0.003 L
Ex: Convert 45 cm to km
• km
hm
dam
m
dm
cm
mm
• Move 5 places to the left to get from cm to km
• Therefore, move the decimal point in 45 five
places to the left to convert from cm to km
 45 cm = 0.00045 km
Ex: Convert 5.4 kg to dg
• kg
hg
dag
g
dg
cg
mg
• Move 4 places to the right to get from kg to dg
• Therefore, move the decimal point in 5.4 four
places to the right to convert from kg to dg
 5.4 kg = 54000 dg
Conversions between the U.S.
Customary System and the Metric
System
• Approximate equivalences between the
U.S. Customary System and the Metric
System are needed for conversion
between systems
• Dimensional Analysis will be used to
compute the conversion
Equivalences
• Units of Weight
– 1 oz  28.35 g
– 1 lb  454 g
– 2.2 lb  1 kg
• Units of Capacity
– 1.06 qt  1 L
– 1 gal  3.79 L
• Units of Length
–
–
–
–
1 in = 2.54 cm
3.28 ft  1 m
1.09 yd  1 m
1 mi  1.61 km
Dimensional Analysis
• Dimensional Analysis (also called FactorLabel Method or the Unit Factor Method) is a
problem-solving method that uses the fact
that any number or expression can be
multiplied by one without changing its value
(Multiplication Property of 1 – the Magic One)
• Use the units to dictate
the form of the Magic One
Ex: Convert 130 lbs to kg
(round to the nearest whole number)
• Write the original measurement as a unit
fraction
• Multiply the unit fraction by a magic one –
the form of which is dictated by the units
– the numerator unit is the unit you want
– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
(decimal number)
Ex: Convert 130 lbs to kg
(round to the nearest whole number)
130 lbs
1

1 kg
2 . 2 lbs
= 59.0 kg

130 kg
2 .2
Ex: Convert 60 km to mi
(round to the nearest whole number)
• Write the original measurement as a unit
fraction
• Multiply the unit fraction by a magic one –
the form of which is dictated by the units
– the numerator unit is the unit you want
– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
(decimal number)
Ex: Convert 60 km to mi
(round to the nearest whole number)
60 km
1

1 mi
1 . 61 km
= 37.2 mi
= 37 mi

60 mi
1 . 61
Ex: Convert 5.4 kg to lb
(round to the nearest tenth place)
• Write the original measurement as a unit
fraction
• Multiply the unit fraction by a magic one –
the form of which is dictated by the units
– the numerator unit is the unit you want
– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
(decimal number)
Ex: Convert 5.4 kg to lb
(round to the nearest tenth place)
5 . 4 kg 2 . 2 lb 11 . 88 lb


1
1 kg
1
= 11.88 lb
= 11.9 lb
Ex: Convert 45 cm to in
(round to the nearest tenth place)
• Write the original measurement as a unit
fraction
• Multiply the unit fraction by a magic one –
the form of which is dictated by the units
– the numerator unit is the unit you want
– the denominator unit is the unit you want to
eliminate
• Write your answer in the specified form
(decimal number)
Ex: Convert 45 cm to in
(round to the nearest tenth place)
45 cm
1

1 in
2 . 54 cm
= 17.71 in
= 17.7 in

45 in
2 . 54
Ex: As a practical joke, on the
show Candid Camera, a gas
station listed their price as
$1.79/Liter. People gassing up
thought they were getting a great
deal, but then were outraged when
their total owed came up. WHY?
• What do you notice about the listed price?
• What should we do?
Listed their price as $1.79/Liter.
$ 1 . 79 3 . 79 L

1L
1 gal
$ 6 . 78
1 gal
Ex: The price of a certain
medication is $35 per Liter.
Find the price per fluid ounce.
$ 35
1L
1 qt 1 pt 1 C
$ 35





1 L 1 . 06 qt 2 pt 2 C 8 fl oz 33 . 92 fl oz
But now what? There isn’t a direct equivalence from Liters to fluid ounces.
We can use several equivalences stepping down to fluid ounces
Liters  Quarts  Pints  Cups  fluid ounces
 $ 1 . 03 / fl oz