understanding and using the metric system. i. advantages of the metric system for science a....
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UNDERSTANDING AND USING THE METRIC SYSTEM
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE
A. INTERNATIONAL STANDARDS B. EASE OF RECORDING C. EASE OF CALCULATIONS
II. UNITS OF MEASUREMENTIII. THE IMPORTANCE OF PREFIXES
IV. IMAGES OF THE VERY LARGE AND VERY SMALL
A. DEFINED UNITS B. DERIVED UNITSA. NANO- TO PICO- THE COMMONLY
USED PREFIXES B. CONVERTING UNITS BY MOVING THE DECIMALA. Extreme images B. THE POWERS OF TEN
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
A. INTERNATIONAL STANDARDS B. EASE OF RECORDING
C. EASE OF CALCULATIONS
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
* All metric system units are based on very specific definitions which are internationally known standards and are precisely reproducable… *
Length =1.0 meter
Volume =1.0 liter
A. INTERNATIONAL STANDARDS… *
THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE WORLD…REGARDLESS OF COUNTRY, LANGUAGE, OR DISCIPLINE… *
Mass = 1.0 kilogram
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
•All metric system units are based on TENS, that is subdivisions of the main units are based on ‘tenths’, ‘hundreths’, thousandths’, etc.
B. EASE OF RECORDING MEASUREMENTS… *
One whole unit.1 unit
(subdivisions can be subdivided again for more precision…but
again by tenths…)
.1 unit.01 unit
.001 unit
This means that very precise measurements can be recorded as
“DECIMAL VALUES” !!
.1 unit.01 unit
.001 unit
EXAMPLES: 5.613 grams5.45 centimeters.802 meters9.023 meters2.351 liters
This is a huge advantage over the older “fraction” based systems…
1/12 unit1/2 unit1/16 unit
Recording measurements is too complex, prone to errors…
Examples:5 yards, 2 feet, 7 1/16 inch4 gallons, 1 quart, 5 ¾ ounces2 pounds, 8 9/32 ounce2 miles, 235 yards, 2 feet, 7 inches
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
•Since almost all measurements done by scientists are intended to be used in math formulas…
C. EASE OF PERFORMING MATH FUNCTIONS… *
•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…
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
C. EASE OF PERFORMING MATH FUNCTIONS… *
Examples:
Is far easier to do than…
1.62 kg(5.4 cm) (8.65 cm) (362 cm)
(1 lb., 9 ½ oz.)(11 ¾ in)(1 ft.4 11/16 in)(1 yd.1ft 1½ in)
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
B. DERIVED UNITS
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
SOME QUANTITIES HAVE TO BE THE STARTING POINTS…
THAT IS, SOME BASIC UNITS HAVE TO BE DEFINED…
THE “BASE” UNITS:The unit of LENGTH: the METER– originally defined as ONE TEN-MILLIONTH the distance from NORTH POLE TO EQUATOR
#1:
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:The unit of VOLUME: the LITER… defined as the space occupied by a cube measuring .1m x .1m x .1m (1 cubic decimeter—1.0 dm3)
1 DECIM
ETER
1 D
EC
IME
TE
R
1 DECIMETER
#2
1 liter = 1dm3
II.UNITS OF MEASUREMENTA. DEFINED UNITS
THE “BASE” UNITS:
(since the cube is 1 dm x 1dm x 1dm, its volume = 1 dm3 )
10 ce
ntimete
rs
10 c
enti
met
ers
10 centimeters
#2
1 liter = 1dm3 also = 1000 cm3
(and since 1 dm = 10 cm, its volume ( 10 cm x 10 cm x 10 cm) also = 1000 cm3 )
II.UNITS OF MEASUREMENTA. DEFINED UNITS
THE “BASE” UNITS:
Since the cube’s volume is 1000 cm3 , 1/1000th of its volume = 1 cm3
#2
1 milliliter = 1 cm3
Using ‘prefixes’, 1/1000th of a liter = 1 millilter; then 1 cm3 = 1 ml
II.UNITS OF MEASUREMENT
A. DEFINED UNITS
THE “BASE” UNITS:
The unit of MASS: the KILOGRAM… defined as the mass of 1.0 liter of pure water at 4.0oC…
1.0 kilogram = mass of 1 liter of H2O
Since .001 L = 1 cm3, then 1
cm3 of water = .001 kg = 1.0
gr
#3
II.UNITS OF MEASUREMENT
b. DERIVED UNITS
UNITS THAT ARE FOUND AS THE RESULT OF CALCULATIONS…
1. The unit of DENSITY: the MASS PER VOLUME…that is, what is the mass of 1.0 cm3 (or 1.0 dm3)of a substance?
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
m = 15 g
V = 5.0 cm3
Divide the mass by the volume…
Density =15 grams5.0 cm3
= 3.0
Divide numbers to get ½ of the
answer
Divide units to get the other ½ of the answer
Grams/cm3
Divide the mass by the volume…
Density =15 grams5.0 cm3
= 3.0
Grams/cm3
This new, more complex unit is
called a ‘derived’ unit…
The ‘division’ slash is read as
“per”…
When two values are multiplied, their units multiply also…
(5.0 kilograms) (7.0 meters)
= 35
Kgm
The ‘derived’ unit is read as “kilogram meter” or
“kilogram dot meter”
Numeric value
• = “x” symbol for
multiplcation
If two numbers which have the same units are to be multiplied…
(5.0 seconds) (3.0 seconds)
= 15
Sec2
The ‘derived’ unit is read as “seconds squared”…
Numeric value
For example,
Some more complex calculations may require both mul. and div…
(8.0 kg) (6.0 meters)
= 12
Sec2
The ‘derived’ unit is read as
“kilogram meter per second
squared”… Numeric value
(2.0 sec) (2.0 sec)
kgm
For example,
Some more complex calculations may require both mul. and div…
(8.0 kg) (6.0 meters)
= 12 Sec2
When the ‘derived’ unit is complex, it may
be assigned a ‘nickname’…
(2.0 sec) (2.0 sec)
kgm This unit is defined as a
“NEWTON”… a unit of force.
= 12 Newtons
III. THE IMPORTANCE OF PREFIXES
•A. FROM NANO TO PICO•B. MOVING THE DECIMAL
III. THE IMPORTANCE OF PREFIXES•A. FROM NANO TO PICOTHE PREFIXES USED ARE COMMON
TO ALL TYPES OF MEASUREMENT:
EXAMPLES:microgram micrometer microliter microvolt
kilogram kilometer kiloliter kilojoule
milligram millimeter milliliter milliamp millisecond
III. THE IMPORTANCE OF PREFIXES•A. FROM NANO TO PICO
Important prefixes to know:
BASE UNIT DECA 10x
HECTA 100x KILO 1000x MEGA 1,000,000x
GIGA 1,000,000,000
DECI .1CENTI .01
MILLI .001 MICRO .000 001
. NANO .000 000 001
The base of any defined or
derived unit
A prefix that makes a unit 10x larger
than the base
This prefix changes the
base into a unit 100x larger
This prefix changes the
base into a unit 1000x larger
This prefix changes the base
into a unit 1,000,000x
larger
This prefix changes the base
into a unit 1,000,000,000x
larger
This prefix changes the
base into a unit 1/10 as large as
the base
This prefix changes the
base into a unit 1/100 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
This prefix changes the base
into a unit 1/1,000,000,000 as large as the
base
Understanding prefixes…Let this entire box represent 1.0 liter…
1/10th (.1) of the box could be called a ‘deciliterHow many of these
would be in 1 liter?in 5 liter?Did you answer 10 ? Then 50?
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?
Understanding prefixes…
That is the secret of converting to more convienent units within the metric system!!
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… that’s really all there is to conversion!!
Understanding prefixes…
If this little box represents 1/1000th of the liter, what could it be called? milliliter??
how many of these are in the 1.0 liter? 1000? What did you do to get that answer?
1.0 00 = 1000 ml
Simply move the decimal 3 places to the right and fill in with zero’s (make a number 1000x bigger…)
move the decimal to the right and fill in the zero’s
BASE UNIT
DECA 10x HECTA 100x
KILO 1000x
MEGA 1,000,000x GIGA 1,000,000,000
DECI .1CENTI .01
MILLI .001
MICRO .000 001 NANO .000 000 001
To change to a smaller unit,
To change to a larger unit move the decimal to the left and fill in the zero’s
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…
“54,500 METERS” can be shortened by changing the unit from ‘meters’ to ‘kilometers’
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!!!
SAMPLE PROBLEM:
BASE UNIT
DECA 10x HECTA 100x
KILO 1000x
MEGA 1,000,000x GIGA 1,000,000,000
DECI .1CENTI .01
MILLI .001
MICRO .000 001 NANO .000 000 001
To change to a larger unit move the decimal to the left and fill in the zero’s
METER
KILOMETER
REMEMBER…
54,500 METERS = 54.5 KILOMETERS
A physics student has this value for the current in a circuit:
14.3 amps
SAMPLE PROBLEM:
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:
move the decimal to the right and fill in the zero’s
BASE UNIT
DECA 10x HECTA 100x
KILO 1000x
MEGA 1,000,000x GIGA 1,000,000,000
DECI .1CENTI .01
MILLI .001
MICRO .000 001 NANO .000 000 001
To change to a smaller unit,
amps
milliamps
14.3 amps
SAMPLE PROBLEM:
14.3 0 0, milliamps.
Converts to:
IV. IMAGES THE VERY LARGE AND VERY SMALL-POWERS OF 10
A. THE COSMOS— astronomical imagesB. SUB-
MICROSCOPIC-- atm imageS
C. WEB SITES-POWERS OF 10
A. THE COSMOS— astronomical images
B. SUB-MICROSCOPIC-- atm imageS
Approx. 1 micrometer (.000 001m)
Image formed by an ‘ATOMIC FORCE MICROSCOPE’…
Approx. 1.5 m
Trenches etched onto a silicon wafer by exposure to an electron beam…
Lesson Plan 1: Metric
SystemPowers of ten animation:
http://www.wordwizz.com/pwrsof10.htm
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/