Understanding and using the metric system
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UNDERSTANDING AND USING THE METRIC SYSTEM. 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. I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE.

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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


I advantages of the metric system for scientific measurement

A. INTERNATIONAL STANDARDS… MEASUREMENT*

* All metric system units are based on very specific definitions which are internationally known standards and are precisely reproducable… *

Volume =1.0 liter

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE WORLD…REGARDLESS OF COUNTRY, LANGUAGE, OR DISCIPLINE… *

Length =1.0 meter

Mass = 1.0 kilogram


I advantages of the metric system for scientific measurement1

B. EASE OF RECORDING MEASUREMENTS… MEASUREMENT*

  • All metric system units are based on TENS, that is subdivisions of the main units are based on ‘tenths’, ‘hundreths’, thousandths’, etc.

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

.1 unit

One whole unit


Subdivisions can be subdivided again for more precision but again by tenths
(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
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
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


I advantages of the metric system for scientific measurement2

C. EASE OF PERFORMING MATH FUNCTIONS… systems…*

  • Since almost all measurements done by scientists are intended to be used in math formulas…

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

  • 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 measurement3

C. EASE OF PERFORMING MATH FUNCTIONS… systems…*

Examples:

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

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
II.UNITS OF MEASUREMENT systems…

A. DEFINED UNITS

B. DERIVED UNITS


Ii units of measurement1
II.UNITS OF MEASUREMENT systems…

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 measurement2
II.UNITS OF MEASUREMENT systems…

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 measurement3
II.UNITS OF MEASUREMENT systems…

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 measurement4
II.UNITS OF MEASUREMENT systems…

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 measurement5
II.UNITS OF MEASUREMENT systems…

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 measurement6
II.UNITS OF MEASUREMENT systems…

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 systems…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 systems… 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 systems… 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 systems…

When two values are multiplied, their units multiply also…

(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

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”…

kgm

= 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.

kgm

= 12

Sec2

= 12 Newtons


Iii the importance of prefixes
III. THE IMPORTANCE OF PREFIXES div…

  • A. FROM NANO TO PICO

  • B. MOVING THE DECIMAL


Iii the importance of prefixes1

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


Iii the importance of prefixes2

This prefix changes the base into a unit 1000x larger div…

  • A. FROM NANO TO PICO

III. THE IMPORTANCE OF PREFIXES

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


Understanding prefixes

Let this entire box represent 1.0 liter… div…

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 prefixes1
Understanding prefixes… div…

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 prefixes2
Understanding prefixes… div…

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


GIGA div…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 .000 001

NANO .000 000 001


Sample problem
SAMPLE PROBLEM: div…

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’


GIGA div…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…

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 problem1
SAMPLE PROBLEM: div…

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 div…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 .000 001

NANO .000 000 001


Sample problem2
SAMPLE PROBLEM: div…

14.3 amps

Converts to:

.

14.3

,

0

0

milliamps


Iv images the very large and very small powers of 10
IV. IMAGES THE VERY LARGE AND VERY SMALL-POWERS OF 10 div…

A. THE COSMOS— astronomical images

B. SUB-MICROSCOPIC-- atm imageS

C. WEB SITES-POWERS OF 10



B sub microscopic atm images
B. SUB-MICROSCOPIC- div…- atm imageS


Approx 1 micrometer 000 001m
Approx. 1 micrometer (.000 001m) div…

Image formed by an ‘ATOMIC FORCE MICROSCOPE’…


Approx. 1.5 div…m

Trenches etched onto a silicon wafer by exposure to an electron beam…


Lesson plan 1 metric system
Lesson Plan 1: Metric System div…

Powers of ten animation:

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

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


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