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**UNDERSTANDING AND USING THE METRIC SYSTEM**

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**A. DEFINED UNITS B. DERIVED UNITS **

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 WORLD…REGARDLESS 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 precision…but 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: 2.351 liters .802 meters 5.45 centimeters 9.023 meters 5.613 grams

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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: 2 miles, 235 yards, 2 feet, 7 inches 2 pounds, 8 9/32 ounce 4 gallons, 1 quart, 5 ¾ ounces 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… #1: 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: #2 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 DECIMETER 1 DECIMETER 1 liter = 1dm3 1 DECIMETER

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**II.UNITS OF MEASUREMENT**

A. DEFINED UNITS #2 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 #2 THE “BASE” UNITS: Using ‘prefixes’, 1/1000th of a liter = 1 millilter; then 1 cm3 = 1 ml Since the cube’s volume is 1000 cm3 , 1/1000th of its volume = 1 cm3 1 milliliter = cm3

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**II.UNITS OF MEASUREMENT**

A. DEFINED UNITS #3 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 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 VOLUME…that 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) = 35 Kgm Numeric value The ‘derived’ unit is read as “kilogram meter” or “kilogram dot meter”

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**The ‘derived’ unit is read as “seconds squared”…**

If two numbers which have the same units are to be multiplied… For example, (5.0 seconds) (3.0 seconds) = 15 Sec2 The ‘derived’ unit is read as “seconds squared”… Numeric value

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**The ‘derived’ unit is read as “kilogram meter per second squared”…**

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”… kgm = 12 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. kgm = 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 1/1000 as large as the base This prefix changes the base into a unit 1/10 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 . NANO

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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… that’s 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 zero’s (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. = 1000 ml

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**To change to a smaller unit, **

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 zero’s MEGA 1,000,000x KILO 1000x HECTA 100x DECA 10x move the decimal to the right and fill in the zero’s BASE UNIT DECI .1 CENTI .01 MILLI .001 MICRO NANO

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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… DECI .1 To change to a larger unit move the decimal to the left and fill in the zero’s CENTI .01 MILLI .001 MICRO NANO

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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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**To change to a smaller unit,**

GIGA 1,000,000,000 To change to a smaller unit, MEGA 1,000,000x KILO 1000x move the decimal to the right and fill in the zero’s HECTA 100x DECA 10x BASE UNIT amps DECI .1 CENTI .01 milliamps MILLI .001 MICRO NANO

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SAMPLE PROBLEM: 14.3 amps Converts to: . 14.3 , 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 ( m) 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**

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