UNDERSTANDING AND USING THE METRIC SYSTEM

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UNDERSTANDING AND USING THE METRIC SYSTEM
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• I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE

A. INTERNATIONAL STANDARDS B. EASE OF RECORDING
C. EASE OF CALCULATIONS
II. UNITS OF MEASUREMENT
III. THE IMPORTANCE OF PREFIXES
A. DEFINED UNITS B. DERIVED UNITS
A. NANO- TO PICO- THE COMMONLY USED PREFIXES
B. CONVERTING UNITS BY
MOVING THE DECIMAL
IV. IMAGES OF THE VERY LARGE AND VERY SMALL
A. Extreme images B. THE POWERS OF TEN
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I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC
MEASUREMENT
A. INTERNATIONAL STANDARDS
B. EASE OF RECORDING
C. EASE OF CALCULATIONS
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I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC
MEASUREMENT
A. INTERNATIONAL STANDARDS
All metric system units are based on very
specific definitions which are internationally
known standards and are precisely reproducable

Volume 1.0 liter
THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE
WORLDREGARDLESS OF COUNTRY, LANGUAGE, OR
DISCIPLINE
Length 1.0 meter
Mass 1.0 kilogram
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I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC
MEASUREMENT
B. EASE OF RECORDING MEASUREMENTS

• All metric system units are based on TENS, that
  is subdivisions of the main units are based on
  tenths, hundreths, thousandths, etc.

.1 unit
One whole unit
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(subdivisions can be subdivided again for more
precisionbut again by tenths)
.1 unit
.01 unit
.001 unit
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This means that very precise measurements can be
recorded as DECIMAL VALUES !!
.1 unit
.01 unit
.001 unit
EXAMPLES
5.613 grams
5.45 centimeters
.802 meters
9.023 meters
2.351 liters
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This is a huge advantage over the older
fraction based systems
Recording measurements is too complex, prone to
errors
1/12 unit
1/16 unit
1/2 unit
Examples
4 gallons, 1 quart, 5 ¾ ounces
2 pounds, 8 9/32 ounce
2 miles, 235 yards, 2 feet, 7 inches
5 yards, 2 feet, 7 1/16 inch
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I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC
MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS

• Since almost all measurements done by scientists
  are intended to be used in math formulas

• It is important that measurements be recorded
  carefully, and with as much precision as
  possible.

• With numbers that are easily manipulated, and/or
  entered into calculators

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I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC
MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS
Examples
1.62 kg
(5.4 cm) (8.65 cm) (362 cm)
Is far easier to do than
(1 lb., 9 ½ oz.)
(11 ¾ in)(1 ft.4 11/16 in)(1 yd.1ft 1½ in)
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
B. DERIVED UNITS
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE BASE UNITS
SOME QUANTITIES HAVE TO BE THE STARTING POINTS
THAT IS, SOME BASIC UNITS HAVE TO BE DEFINED
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The unit of LENGTH the METER originally defined
as ONE TEN-MILLIONTH the distance from NORTH POLE
TO EQUATOR
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE BASE UNITS
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The unit of VOLUME the LITER defined as the
space occupied by a cube measuring .1m x .1m x
.1m (1 cubic decimeter1.0 dm3)
1 DECIMETER
1 DECIMETER
1 liter 1dm3
1 DECIMETER
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
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THE BASE UNITS
(since the cube is 1 dm x 1dm x 1dm, its volume
1 dm3 )
(and since 1 dm 10 cm, its volume ( 10 cm
x 10 cm x 10 cm) also 1000 cm3 )
10 centimeters
1 liter 1dm3 also 1000 cm3
10 centimeters
10 centimeters
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
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THE BASE UNITS
Since the cubes volume is 1000 cm3 , 1/1000th
of its volume 1 cm3
Using prefixes, 1/1000th of a liter 1
millilter then 1 cm3 1 ml
1 milliliter 1 cm3
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II.UNITS OF MEASUREMENT
A. DEFINED UNITS
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THE BASE UNITS
1.0 kilogram mass of 1 liter of H2O
The unit of MASS the KILOGRAM defined as the
mass of 1.0 liter of pure water at 4.0oC
Since .001 L 1 cm3, then 1 cm3 of water
.001 kg 1.0 gr
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II.UNITS OF MEASUREMENT
b. DERIVED UNITS
UNITS THAT ARE FOUND AS THE RESULT OF
CALCULATIONS
1. The unit of DENSITY the MASS PER VOLUMEthat
is, what is the mass of 1.0 cm3 (or 1.0 dm3)of a
substance?
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To calculate DENSITY divide the MASS by the
VOLUME
If, for example, an object has a mass of 15 grams
and occupies a volume of 5.0 cm3,
Mass 15 grams
Volume 5.0 cm3
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Divide the mass by the volume
15 grams
3.0
Grams/cm3
Density
5.0 cm3
Divide numbers to get ½ of the answer
Divide units to get the other ½ of the answer
m 15 g
V 5.0 cm3
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Divide the mass by the volume
15 grams
3.0
Grams/cm3
Density
5.0 cm3
The division slash is read as per
This new, more complex unit is called a derived
unit
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x symbol for multiplcation
When two values are multiplied, their units
multiply also
(5.0 kilograms)? (7.0 meters)
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Kg?m
Numeric value
The derived unit is read as kilogram meter or
kilogram dot meter
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If two numbers which have the same units are to
be multiplied
For example,
(5.0 seconds)? (3.0 seconds)
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Sec2
The derived unit is read as seconds squared

Numeric value
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Some more complex calculations may require both
mul. and div
For example,
(8.0 kg)? (6.0 meters)
(2.0 sec)? (2.0 sec)
The derived unit is read as kilogram meter per
second squared
kg?m
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Sec2
Numeric value
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Some more complex calculations may require both
mul. and div
(8.0 kg)? (6.0 meters)
(2.0 sec)? (2.0 sec)
When the derived unit is complex, it may be
assigned a nickname
This unit is defined as a NEWTON a unit of
force.
kg?m
12
Sec2
12 Newtons
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III. THE IMPORTANCE OF PREFIXES

• A. FROM NANO TO PICO

• B. MOVING THE DECIMAL

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III. THE IMPORTANCE OF PREFIXES

• A. FROM NANO TO PICO

THE PREFIXES USED ARE COMMON TO ALL TYPES OF
MEASUREMENT
EXAMPLES
microgram micrometer microliter microvolt
milligram millimeter milliliter milliamp
millisecond
kilogram kilometer kiloliter kilojoule
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III. THE IMPORTANCE OF PREFIXES
This prefix changes the base into a unit 1000x
larger

• A. FROM NANO TO PICO

A prefix that makes a unit 10x larger than the
base
This prefix changes the base into a unit 100x
larger
The base of any defined or derived unit
This prefix changes the base into a unit
1,000,000,000x larger
GIGA 1,000,000,000
Important prefixes to know
This prefix changes the base into a unit
1,000,000x larger
This prefix changes the base into a unit 1/100 as
large as the base
MEGA 1,000,000x
This prefix changes the base into a unit 1/10 as
large as the base
This prefix changes the base into a unit 1/1000
as large as the base
This prefix changes the base into a unit
1/1,000,000 as large as the base
KILO 1000x
This prefix changes the base into a unit
1/1,000,000,000 as large as the base
HECTA 100x
DECA 10x
BASE UNIT
DECI .1
CENTI .01
MILLI .001
MICRO .000 001
. NANO .000 000 001
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Understanding prefixes
Let this entire box represent 1.0 liter
1/10th (.1) of the box could be called a
deciliter
How many of these would be in 1 liter?
To get those values, did you just multiply by 10?
Did you do a mental short-cut and just tack on a
zero? That is, just slide the decimal over and
fill in with zero?
in 5 liter?
Did you answer 10 ? Then 50?
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Understanding prefixes
If the measured value gets too big (or too
small), change to a more convienent unit by
moving the decimal to the left or to the right,
then fill in zeros thats really all there is to
conversion!!
That is the secret of converting to more
convienent units within the metric system!!
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Understanding prefixes
Simply move the decimal 3 places to the right and
fill in with zeros (make a number 1000x bigger)
If this little box represents 1/1000th of the
liter, what could it be called?
What did you do to get that answer?
how many of these are in the 1.0 liter?
1000?
milliliter??
1.
0
0
0
1000 ml
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GIGA 1,000,000,000
To change to a smaller unit,
To change to a larger unit move the decimal to
the left and fill in the zeros
MEGA 1,000,000x
KILO 1000x
HECTA 100x
DECA 10x
move the decimal to the right and fill in the
zeros
BASE UNIT
DECI .1
CENTI .01
MILLI .001
MICRO .000 001
NANO .000 000 001
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SAMPLE PROBLEM
AN ANSWER TO A CALCULATION GAVE A VALUE OF
54,500 METERS
ALTHOUGH CORRECT, THE VALUE IS LARGE AND
CUMBERSOME IT CAN BE SHORTENED AND REDUCED TO A
SMALLER VALUE BY A SIMPLE CONVERSION
METERS are 1000x smaller than KILOMETERS
therefore the converted value will be 1/1000th
the original! That is, move the decimal 3 places
to the left!!!
54,500 METERS can be shortened by changing the
unit from meters to kilometers
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GIGA 1,000,000,000
54,500 METERS
54.5 KILOMETERS
MEGA 1,000,000x
KILO 1000x
KILOMETER
HECTA 100x
DECA 10x
METER
BASE UNIT
REMEMBER
To change to a larger unit move the decimal to
the left and fill in the zeros
DECI .1
CENTI .01
MILLI .001
MICRO .000 001
NANO .000 000 001
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SAMPLE PROBLEM
A physics student has this value for the current
in a circuit 14.3
amps
However, the formula in which she has to use the
value calls for the current in MILLIAMPS
A quick conversion by moving the decimal point is
easy
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GIGA 1,000,000,000
To change to a smaller unit,
MEGA 1,000,000x
move the decimal to the right and fill in the
zeros
KILO 1000x
HECTA 100x
DECA 10x
BASE UNIT
amps
DECI .1
CENTI .01
milliamps
MILLI .001
MICRO .000 001
NANO .000 000 001
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SAMPLE PROBLEM
14.3 amps
Converts to
.
14.3
0
0
,
milliamps
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IV. IMAGES THE VERY LARGE AND VERY SMALL-POWERS
OF 10
A. THE COSMOS astronomical
images
B. SUB-MICROSCOPIC-- atm imageS
C. WEB SITES-POWERS OF 10
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A. THE COSMOS astronomical
images
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B. SUB-MICROSCOPIC-- atm imageS
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Approx. 1 micrometer (.000 001m)
Image formed by an ATOMIC FORCE MICROSCOPE
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Approx. 1.5 ?m
Trenches etched onto a silicon wafer by exposure
to an electron beam
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Lesson Plan 1 Metric
System
Powers of ten animation http//www.wordwizz.com/p
wrsof10.htm http//micro.magnet.fsu.edu/primer/ja
va/scienceopticsu/powersof10/
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