understanding and using the metric system. i. advantages of the metric system for science a....

UNDERSTANDING AND USING THE METRIC SYSTEM

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE

A. INTERNATIONAL STANDARDS B. EASE OF RECORDING C. EASE OF CALCULATIONS

II. UNITS OF MEASUREMENTIII. THE IMPORTANCE OF PREFIXES

IV. IMAGES OF THE VERY LARGE AND VERY SMALL

A. DEFINED UNITS B. DERIVED UNITSA. NANO- TO PICO- THE COMMONLY

USED PREFIXES B. CONVERTING UNITS BY MOVING THE DECIMALA. 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

* 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

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 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: 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

•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…

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

A. DEFINED UNITS

B. DERIVED UNITS

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:

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 decimeter—1.0 dm3)

1 DECIM

ETER

1 D

EC

IME

TE

R

1 DECIMETER

#2

1 liter = 1dm3

II.UNITS OF MEASUREMENTA. DEFINED UNITS

THE “BASE” UNITS:

(since the cube is 1 dm x 1dm x 1dm, its volume = 1 dm3 )

10 ce

ntimete

rs

10 c

enti

met

ers

10 centimeters

#2

1 liter = 1dm3 also = 1000 cm3

(and since 1 dm = 10 cm, its volume ( 10 cm x 10 cm x 10 cm) also = 1000 cm3 )

II.UNITS OF MEASUREMENTA. DEFINED UNITS

THE “BASE” UNITS:

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

#2

1 milliliter = 1 cm3

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

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 4.0oC…

1.0 kilogram = mass of 1 liter of H2O

Since .001 L = 1 cm3, then 1

cm3 of water = .001 kg = 1.0

gr

#3

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?

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

m = 15 g

V = 5.0 cm3

Divide the mass by the volume…

Density =15 grams5.0 cm3

= 3.0

Divide numbers to get ½ of the

answer

Divide units to get the other ½ of the answer

Grams/cm3

Divide the mass by the volume…

Density =15 grams5.0 cm3

= 3.0

Grams/cm3

This new, more complex unit is

called a ‘derived’ unit…

The ‘division’ slash is read as

“per”…

When two values are multiplied, their units multiply also…

(5.0 kilograms) (7.0 meters)

= 35

Kgm

The ‘derived’ unit is read as “kilogram meter” or

“kilogram dot meter”

Numeric value

• = “x” symbol for

multiplcation

If two numbers which have the same units are to be multiplied…

(5.0 seconds) (3.0 seconds)

= 15

Sec2

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

Numeric value

For example,

Some more complex calculations may require both mul. and div…

(8.0 kg) (6.0 meters)

= 12

Sec2

The ‘derived’ unit is read as

“kilogram meter per second

squared”… Numeric value

(2.0 sec) (2.0 sec)

kgm

For example,

Some more complex calculations may require both mul. and div…

(8.0 kg) (6.0 meters)

= 12 Sec2

When the ‘derived’ unit is complex, it may

be assigned a ‘nickname’…

(2.0 sec) (2.0 sec)

kgm This unit is defined as a

“NEWTON”… a unit of force.

= 12 Newtons

III. THE IMPORTANCE OF PREFIXES

•A. FROM NANO TO PICO•B. MOVING THE DECIMAL

III. THE IMPORTANCE OF PREFIXES•A. FROM NANO TO PICOTHE PREFIXES USED ARE COMMON

TO ALL TYPES OF MEASUREMENT:

EXAMPLES:microgram micrometer microliter microvolt

kilogram kilometer kiloliter kilojoule

milligram millimeter milliliter milliamp millisecond

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 .1CENTI .01

MILLI .001 MICRO .000 001

. NANO .000 000 001

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

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?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?

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 conversion!!

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…)

move the decimal to the right and fill in the zero’s

BASE UNIT

DECA 10x HECTA 100x

KILO 1000x

MEGA 1,000,000x GIGA 1,000,000,000

DECI .1CENTI .01

MILLI .001

MICRO .000 001 NANO .000 000 001

To change to a smaller unit,

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

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:

BASE UNIT

DECA 10x HECTA 100x

KILO 1000x

MEGA 1,000,000x GIGA 1,000,000,000

DECI .1CENTI .01

MILLI .001

MICRO .000 001 NANO .000 000 001

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

METER

KILOMETER

REMEMBER…

54,500 METERS = 54.5 KILOMETERS

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

BASE UNIT

DECA 10x HECTA 100x

KILO 1000x

MEGA 1,000,000x GIGA 1,000,000,000

DECI .1CENTI .01

MILLI .001

MICRO .000 001 NANO .000 000 001

To change to a smaller unit,

amps

milliamps

14.3 amps

SAMPLE PROBLEM:

14.3 0 0, milliamps.

Converts to:

IV. IMAGES THE VERY LARGE AND VERY SMALL-POWERS OF 10

A. THE COSMOS— astronomical imagesB. SUB-

MICROSCOPIC-- atm imageS

C. WEB SITES-POWERS OF 10

A. THE COSMOS— astronomical images

B. SUB-MICROSCOPIC-- atm imageS

Approx. 1 micrometer (.000 001m)

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

SystemPowers of ten animation:

http://www.wordwizz.com/pwrsof10.htm

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