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### I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

### I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

### I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

### I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

A. INTERNATIONAL STANDARDS B. EASE OF RECORDINGC. EASE OF CALCULATIONS

II. UNITS OF MEASUREMENT

III. THE IMPORTANCE OF PREFIXES

A. DEFINED UNITS B. DERIVED UNITS

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE

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

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

A. INTERNATIONAL STANDARDS

B. EASE OF RECORDING

C. EASE OF CALCULATIONS

* 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

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

.01 unit

.001 unit

This means that very precise measurements can be recorded as “DECIMAL VALUES” !!

.1 unit

.01 unit

.001 unit

EXAMPLES:

2.351 liters

5.45 centimeters

.802 meters

5.613 grams

9.023 meters

This is a huge advantage over the older “fraction” based systems…

Recording measurements is too complex, prone to errors…

1/12unit

1/16 unit

1/2unit

Examples:

2 miles, 235 yards, 2 feet, 7 inches

4 gallons, 1 quart, 5 ¾ ounces

2 pounds, 8 9/32 ounce

5 yards, 2 feet, 7 1/16 inch

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…

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)

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

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

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

II.UNITS OF MEASUREMENT

A. DEFINED UNITS

#2

THE “BASE” UNITS:

Since the cube’s volume is 1000 cm3 , 1/1000th of its volume = 1 cm3

Using ‘prefixes’, 1/1000th of a liter = 1 millilter; then 1 cm3 = 1 ml

1 milliliter = 1 cm3

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 1 cm3 of water = .001 kg = 1.0 gr

II.UNITS OF MEASUREMENT

b. DERIVED UNITS

UNITS THAT ARE FOUND AS THE RESULT OF CALCULATIONS…

1. The unit of DENSITY: the MASSPER 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

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

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…

• = “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”

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

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

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

III. THE IMPORTANCE OF PREFIXES

THE PREFIXES USED ARE COMMON TO ALL TYPES OF MEASUREMENT:

EXAMPLES:

microgram micrometer microliter microvolt

milligram millimeter milliliter milliamp millisecond

kilogram kilometer kiloliter kilojoule

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 .000 001

. NANO .000 000 001

Let this entire box represent 1.0 liter…

Understanding prefixes…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?

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!!

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.

0

0

0

= 1000 ml

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 .000 001

NANO .000 000 001

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’

54,500 METERS

= 54.5 KILOMETERS

MEGA 1,000,000x

KILO 1000x

KILOMETER

HECTA 100x

DECA 10x

METER

BASE UNIT

REMEMBER…

To change to a larger unit move the decimal to the left and fill in the zero’s

DECI .1

CENTI .01

MILLI .001

MICRO .000 001

NANO .000 000 001

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:

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 .000 001

NANO .000 000 001

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

Approx. 1 micrometer (.000 001m)

Image formed by an ‘ATOMIC FORCE MICROSCOPE’…

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/pwrsof10.htm

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

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