UNDERSTANDING AND USING THE METRIC SYSTEM I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE...
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Transcript of UNDERSTANDING AND USING THE METRIC SYSTEM I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE...
UNDERSTANDING AND USING THE METRIC SYSTEM
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE
A. INTERNATIONAL STANDARDS
B. EASE OF RECORDINGC. EASE OF CALCULATIONS
II. THE IMPORTANCE OF PREFIXES
A. MILLI - TO KILO - THE COMMONLY USED PREFIXES
B. CONVERTING UNITS BY MOVING THE DECIMAL
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT
* All metric system units are based on specific definitions which are internationally known standards and are reproducible
Length =1.0 meter
Volume =1.0 liter
A. INTERNATIONAL STANDARDS… *
*THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE WORLD… REGARDLESS OF COUNTRY OR LANGUAGE
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 divided again and again for more
precision….1 unit
.01 unit
.001 unit
(Again by tenths)
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
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
II.UNITS OF MEASUREMENT
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
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 MEASUREMENT
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
#3
II.UNITS OF MEASUREMENT
THE “BASE” UNITS:
The unit of TIME: the SECOND…
#4
III. THE IMPORTANCE OF PREFIXES
•A. FROM MILLI TO KILO
•B. MOVING THE DECIMAL
III. THE IMPORTANCE OF PREFIXES•A. FROM MILLI TO KILO
THE PREFIXES USED ARE COMMON TO ALL TYPES OF MEASUREMENT:
EXAMPLES:
gram meter liter volt
kilogram kilometer kiloliter kilojoule
milligram millimeter milliliter milliamp millisecond
III. THE IMPORTANCE OF PREFIXES•A. FROM MILLI TO KILO
Important prefixes to know:
BASE UNIT DECA 10x
HECTA 100x KILO 1000x
DECI .1CENTI .01
MILLI .001
The base of any defined or
derived unitA 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 1/10 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
Milk
Chocolate
Drinking
Died
Henry
King
BASE UNIT
DECA
HECTA
KILO
DECI
CENTI
MILLICome up
with a sentence to order
the prefixes!
How are we going
to remember
these?
My
Cat
Died
Drinking
Holy
Ketchup
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?
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?
Did you answer 10?Who thinks 50?
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 conversions!!
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…)
BASE UNIT
DECA
HECTA
KILO
DECI
CENTI
MILLITo change to a smaller unit move the decimal to the right and fill in the zero’s
To change to a larger unit move the decimal to the left and fill in the zero’s
Down and to the LEFT
That is…
Up and to the RIGHT
That is…
That is…
Up and to the RIGHT
That is…
Down and to the LEFT
That is…
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:
To change to a larger unit move the decimal to the left and fill in the zero’s
METER
KILOMETER
REMEMBER…
MILLICENTIDECI BASE UNIT DEKAHECTO KILO
54,500
54.500
Use the chart…
MILLICENTIDECI BASE UNIT DEKAHECTO KILO
5450.0545.00
METER
KILOMETER
REMEMBER…
54,500 METERS
= 54.5 KILOMETERS
MILLICENTIDECI BASE UNIT DEKAHECTO KILO
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
To change to a smaller unit,
amps
milliampsMILLICENTIDECI BASE UNIT DEKAHECTO KILO
14.3
14300
Use the chart…
MILLICENTIDECI BASE UNIT DEKAHECTO KILO
1431430
14.3 amps
SAMPLE PROBLEM:
14.3 0 0 .
Converts to:
= 14300 milliamps
SAMPLE PROBLEM:
SAMPLE PROBLEM:
Metric Activity
1. Length of your shoe in mm
2. Your height in dm
3. Width of the hallway in meters
4. Circumference of your head in cm
5. Area of your desk in cm2
Shoe (mm) Height (dm) Hallway (m) Head (cm) Desk (cm2)
290 180 3 55 7830
315 7.5 2.7 51 8056
320 17.2 3 58.5 8056
290 17 2.99 57 8056
330 18.4 3.3 63 17,422.5
300 17.6 3.3 60 17,422.5
240 12.1 2.69 57 7830
270 14.9 2.67 51.5 8,258.25
270 15.3 2.7 54 7830
3000 1600 2.5 460 16100
220 15.7 2.31 51 8056
25 1560 2.7 58 16695
248 1400 2.7 54 78.3000
301 16.9 2.99 50 8056
310 18 2.99 55 8056
260 165 2.99 50 16100
260 164 2.99 51 15812
270 163 3.1 54.5 15812
210 15.5 3 54 95.6
Now find...
1. Class shoe length in meters
2. Average height in cm
3. Average head size in dm
Shoe (mm) Height (dm) Hallway (m) Head (cm) Desk (cm2)
225 14.85 3.055 54 16,192
325 17.4 3.01 56.3 16,192
250 15.8 3.06 55 14,352
320 18.8 3.08 57.5 8082.5
250 15.5 3.02 48 14,352
300 17.8 3.01 56 1620
320 16.2 3.5 57 7750
240 15.0 3.08 55 8082.5
320 17 3.5 55 7750
250 16.2 3.1 58.5 7,705
1. Class shoe length in meters
2. Average height in cm
3. Average head size in dm
SAMPLE PROBLEM:
Sometimes numbers can still be quite large or quite small
For this scientists use scientific notation
65,000,000,000,000 km
.0000000000001 mm
Scientific Notation
The number must be expressed so only a single digit remains to either the right or left of the decimal point
65,000 = 6.5 x10 4
Scientific Notation
The power of 10 is the number of places the decimal place must be shifted
65,000 = 6.5 x10 4
Scientific Notation
If the decimal point is shifted left the exponent is positive
65,000 = 6.5 x10 4
Scientific Notation
If the decimal point is shifted right the exponent is negative
0.0001 = 1.0 x10 -4
Scientific Notation
0.007 = 7.0 x 10
4,500,000 = 4.5 x 10
167,000 =
.000046 =
6?
?-3
1.67 x 105
4.6 x 10-5