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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 IV. IMAGES OF THE VERY LARGE AND VERY SMALL A. DEFINED UNITS B. DERIVED UNITS A. NANO- TO PICO- THE COMMONLY USED PREFIXES B. CONVERTING UNITS BY MOVING THE DECIMAL 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 * 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

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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

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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: grams5.45 centimeters.802 meters9.023 meters2.351 liters

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This is a huge advantage over the older fraction based systems… 1/12 unit 1/2 unit 1/16 unit Recording measurements is too complex, prone to errors… Examples: 5 yards, 2 feet, 7 1/16 inch 4 gallons, 1 quart, 5 ¾ ounces2 pounds, 8 9/32 ounce2 miles, 235 yards, 2 feet, 7 inches

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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…

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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)

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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 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:

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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 decimeter1.0 dm 3 ) 1 DECIMETER #2 1 liter = 1dm 3

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II.UNITS OF MEASUREMENT A. DEFINED UNITS THE BASE UNITS: (since the cube is 1 dm x 1dm x 1dm, its volume = 1 dm 3 ) 10 centimeters #2 1 liter = 1dm 3 also = 1000 cm 3 (and since 1 dm = 10 cm, its volume ( 10 cm x 10 cm x 10 cm) also = 1000 cm 3 )

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II.UNITS OF MEASUREMENT A. DEFINED UNITS THE BASE UNITS: Since the cubes volume is 1000 cm 3, 1/1000 th of its volume = 1 cm 3 #2 1 milliliter = 1 cm 3 Using prefixes, 1/1000 th of a liter = 1 millilter; then 1 cm 3 = 1 ml

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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 4.0 o C… 1.0 kilogram = mass of 1 liter of H 2 O Since.001 L = 1 cm 3, then 1 cm 3 of water =.001 kg = 1.0 gr #3

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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 cm 3 (or 1.0 dm 3 )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 cm 3, Mass = 15 grams Volume = 5.0 cm 3

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m = 15 g V = 5.0 cm 3 Divide the mass by the volume … Density = 15 grams 5.0 cm 3 = 3.0 Divide numbers to get ½ of the answer Divide units to get the other ½ of the answer Grams/cm 3

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Divide the mass by the volume … Density = 15 grams 5.0 cm 3 = 3.0 Grams/cm 3 This new, more complex unit is called a derived unit… The division slash is read as per…

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When two values are multiplied, their units multiply also… (5.0 kilograms) (7.0 meters) = 35 Kg m The derived unit is read as kilogram meter or kilogram dot meter Numeric value = x symbol for multiplcation

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If two numbers which have the same units are to be multiplied… (5.0 seconds) (3.0 seconds) = 15 Sec 2 The derived unit is read as seconds squared… Numeric value For example,

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Some more complex calculations may require both mul. and div… (8.0 kg) (6.0 meters) = 12 Sec 2 The derived unit is read as kilogram meter per second squared… Numeric value (2.0 sec) kg m For example,

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Some more complex calculations may require both mul. and div… (8.0 kg) (6.0 meters) = 12 Sec 2 When the derived unit is complex, it may be assigned a nickname… (2.0 sec) kg m This unit is defined as a NEWTON … a unit of force. = 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 kilogram kilometer kiloliter kilojoule milligram millimeter milliliter milliamp millisecond

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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.1 CENTI.01 MILLI.001 MICRO NANO 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

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Understanding prefixes… Let this entire box represent 1.0 liter… 1/10 th (.1) of the box could be called adeciliter How 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?

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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… thats really all there is to conversion!!

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Understanding prefixes… If this little box represents 1/1000 th 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? 1.000= 1000 ml Simply move the decimal 3 places to the right and fill in with zeros (make a number 1000x bigger…)

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

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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 1/1000 th the original! That is, move the decimal 3 places to the left!!! SAMPLE PROBLEM:

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BASE UNIT DECA 10x HECTA 100x KILO 1000x MEGA 1,000,000x GIGA 1,000,000,000 DECI.1 CENTI.01 MILLI.001 MICRO NANO To change to a larger unit move the decimal to the left and fill in the zeros METER KILOMETE R REMEMBER … 54,500 METERS = 54.5 KILOMETERS

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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:

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

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14.3 amps SAMPLE PROBLEM: , milliamps. Converts to:

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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 Powers of ten animation: eopticsu/powersof10/

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