UNDERSTANDING AND USING THE METRIC SYSTEM I ADVANTAGES

UNDERSTANDING AND USING THE METRIC SYSTEM

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE A. INTERNATIONAL STANDARDS B. EASE OF II. UNITS OF MEASUREMENT RECORDING C. EASE OF DEFINED UNITS B. OF DERIVED III. A. THE IMPORTANCE PREFIXES CALCULATIONS NANO- TO OF PICO-THE COMMONLY USEDAND PREFIXES IV. A. UNITS IMAGES VERY LARGE B. CONVERTING UNITS BY MOVING THE DECIMAL VERY SMALL A. 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 A. INTERNATIONAL STANDARDS… * All metric system units are based on very specific definitions which are Volume =1. 0 liter internationally known standards and are precisely reproducable… * THAT IS, MEASUREMENTS ARE THE SAME ALL=1. 0 OVER THE Length meter Mass = 1. 0 WORLD…REGARDLESS OF COUNTRY, kilogram LANGUAGE, OR DISCIPLINE… * *

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

(subdivisions can be subdivided again for more precision…but again by tenths…). 1 unit. 001 unit

This means that very precise measurements can be recorded as “DECIMAL VALUES” !!. 1 unit. 001 unit EXAMPLES: 2. 351 5. 45. 802 5. 613 meters 9. 023 centimeters liters grams meters

This is a huge advantage over the older “fraction” based systems… Recording measurements is too complex, prone to errors… 1/16 unit 1/2 unit Examples: 1/12 unit 2 miles, gallons, pounds, 235 yards, 18 quart, 9/32 27 feet, ounce 5¾ 7 inches ounces 524 yards, 2 feet, 1/16

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…

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. 1 ft 1½ in)

II. UNITS OF MEASUREMENT A. DEFINED UNITS B. DERIVED UNITS

II. UNITS OF MEASUREMENT A. DEFINED UNITS THE “BASE” UNITS: #1: SOME QUANTITIES HAVE TO BE THEunit STARTING POINTS… The of LENGTH: the METER– originally defined as ONE TENTHAT IS, SOME BASIC UNITS MILLIONTH the distance from HAVE TO BE DEFINED… NORTH POLE TO EQUATOR

II. UNITS OF MEASUREMENT A. DEFINED UNITS #2 ER THE “BASE” UNITS: 1 1 DECIMETER D EC I M ET The unit of VOLUME: the LITER… defined as the space occupied by a cube measuring. 1 m x. 1 m (1 cubic decimeter— 1. 0 dm 3) 1 liter = 1 dm 3 1 DECIMETER

II. UNITS OF MEASUREMENT er nt ce 10 10 centimeters im et (since the cube dm x 1 dm, its (and since 1 dmis=110 cm, its volume 3 ) volume = 1 dm ( 10 cm x 10 cm) also = 1000 cm 3 ) s A. DEFINED UNITS #2 THE “BASE” UNITS: 3 1 dm 1 liter = 3 also = 1000 cm 10 centimeters

II. UNITS OF MEASUREMENT A. DEFINED UNITS #2 THE “BASE” UNITS: Using the Since ‘prefixes’, cube’s volume 1/1000 thisof 1000 a liter cm=3 , 1 1/1000 th of millilter; then its 1 volume cm 3 = = 1 ml 1 cm 3 1 milliliter = cm 3 1

II. UNITS OF MEASUREMENT A. DEFINED UNITS THE “BASE” UNITS: #3 1. 0 kilogram = The unit of MASS: the KILOGRAM… defined as the mass of 1. 0 mass liter ofof 1 pure liter. Lwater Since. 001 = 3, then 1 cm 1 o of H O 2 at 4. 0 C… cm 3 of water =. 001 kg = 1. 0 gr

II. UNITS OF MEASUREMENT b. DERIVED 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?

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

Divide the mass by the volume… Density = m = 15 grams 5. 0 cm 3 = 3. 0 Grams/cm 3 Divide numbers Divide to to get ½units of the get the other ½ answer of the answer V = 5. 0 cm 3

Divide the mass by the volume… Density = 15 grams 5. 0 cm 3 = 3. 0 Grams/cm 3 The ‘division’ This new, more slash iscomplex read as unit is “per”… called a ‘derived’ unit…

= “x” When two values are multiplied, • their units multiply also… symbol for multiplcation (5. 0 kilograms) (7. 0 meters) = 35 Kg m Numeric value The ‘derived’ unit is read as “kilogram meter” or “kilogram dot meter”

If two numbers which have the same units are to be multiplied… For example, (5. 0 seconds) (3. 0 seconds) = 15 Sec 2 ‘derived’ unit is read as Numeric. The value “seconds squared”…

Some more complex calculations may require both mul. and div… For example, (8. 0 kg) (6. 0 meters) (2. 0 sec) = 12 kg m Sec 2 Numeric value The ‘derived’ unit is read as “kilogram meter per second squared”…

Some more complex calculations may require both mul. and div… (8. 0 kg) (6. 0 meters) (2. 0 sec) = 12 kg m Sec 2 = 12 Newtons When This unittheis ‘derived’ unita is defined as “NEWTON”… a complex, it may be assigned unit of force. a ‘nickname’…

III. THE IMPORTANCE OF PREFIXES • A. FROM NANO TO PICO • B. MOVING THE DECIMAL

III. THE IMPORTANCE OF PREFIXES • A. FROM NANO TO PICO THE PREFIXES USED ARE COMMON TO ALL TYPES OF MEASUREMENT: EXAMPLES: milligram millimeter milliliter milliamp millisecond kilogram kilometer kiloliter kilojoule microgram micrometer microliter microvolt

III. THE IMPORTANCE OF PREFIXES • A. FROM NANO TO PICOThis prefix This that prefix A prefix makes changes the base of any GIGA 1, 000, 000 a. The This prefix changes the unit 10 x larger Important to know: , 000 x MEGA 1, 000 prefixes This prefix base into a unit defined or This prefix changes the base into a unit than the base KILO 1000 x This prefix changes the base 1000 x larger derived unit changes the 0 x 10 A CT HE into a 100 x larger changes the DECA 10 x into a base into aunit 1, 000, 000 x base into a a unit BASE UNIT base into a unit 1, 000 x 1/100 as larger 1/1000 1/10 as as large as 1/1, 000 as DECI. 1 1/1, 000, 000 larger as the base CENTI. 01 as the base large as as largethe as base the MILLI. 001 base MICRO. 000 001. NANO. 000 001

Let this entire box Understanding prefixes… represent 1. 0 liter… 1/10 th (. 1) of the box could be called a ‘deciliter How many of these To get those values, would be in 1 liter? Didyou youjust do ain mental 5 liter? short-cut did multiply and 10? just tack. Did on you a zero? That answer 10 ? by is, just slide Then the decimal 50? over and fill in with zero?

Understanding prefixes… If theismeasured That the secretvalue of gets too big (or too small), converting to more change to aunits morewithin the convienent unit by moving metric system!! the decimal to the left or to the right, then fill in zeros… that’s really all there is to conversion!!

Understanding prefixes… Simply move the decimal 3 If this little What places did to the you right dorepresents toand get in fillthe how many ofbox these are th of the liter, what 1/1000 in with zero’s (make a that answer? 1000? 1. 0 liter? milliliter? ? could it be called? number 1000 x bigger…) 1. 0 0 0 = 1000 ml

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

SAMPLE PROBLEM: AN ANSWER TO A CALCULATION GAVE A VALUE OF “ 54, 500 METERS” ALTHOUGH ‘CORRECT’, THE VALUE METERS are 1000 xcan smaller than “ 54, 500 METERS” be IS LARGE AND CUMBERSOME; IT KILOMETERS… therefore the shortened by changing unit CAN BE SHORTENED ANDthe REDUCED th converted value will be 1/1000 TO A SMALLER BY A SIMPLE from ‘meters’ VALUE to ‘kilometers’ CONVERSION… the original! That is, move the decimal 3 places to the left!!!

54, 500 METERS 1, 000, 000 = 54. 5 KILOMETERS GIGA MEGA 1, 000 x KILO 1000 x HECTA 100 x DECA 10 x BASE UNIT DECI. 1 CENTI. 01 MILLI. 001 MICRO. 000 001 NANO. 000 001 KILOMETER REMEMBER… To change to a larger unit move the decimal to the left and fill in the zero’s

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:

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

SAMPLE PROBLEM: 14. 3 amps Converts to: 14. 3 , 0 0. milliamps

IV. IMAGES THE VERY LARGE AND VERY SMALL-POWERS OF 10 A. THE COSMOS— astronomical images B. SUB-MICROSCOPIC-- atm image. S C. WEB SITES-POWERS OF 10

A. THE COSMOS— images astronomical

B. SUB-MICROSCOPIC-atm image. S

Approx. 1 micrometer (. 000 001 m) 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 System Powers of ten animation: http: //www. wordwizz. com/pwrsof 10. htm http: //micro. magnet. fsu. edu/primer/java/scienc eopticsu/powersof 10/