UNDERSTANDING AND USING THE METRIC SYSTEM

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE

A. INTERNATIONAL STANDARDS

B. EASE OF RECORDINGC. EASE OF CALCULATIONS

II. THE IMPORTANCE OF PREFIXES

A. MILLI - TO KILO - THE COMMONLY USED PREFIXES

B. CONVERTING UNITS BY MOVING THE DECIMAL

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENTIFIC MEASUREMENT

* All metric system units are based on specific definitions which are internationally known standards and are reproducible

Length =1.0 meter

Volume =1.0 liter

A. INTERNATIONAL STANDARDS… *

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

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 divided again and again for more

precision….1 unit

.01 unit

.001 unit

(Again by tenths)

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

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

II.UNITS OF MEASUREMENT

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

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 MEASUREMENT

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

#3

II.UNITS OF MEASUREMENT

THE “BASE” UNITS:

The unit of TIME: the SECOND…

#4

III. THE IMPORTANCE OF PREFIXES

•A. FROM MILLI TO KILO

•B. MOVING THE DECIMAL

III. THE IMPORTANCE OF PREFIXES•A. FROM MILLI TO KILO

THE PREFIXES USED ARE COMMON TO ALL TYPES OF MEASUREMENT:

EXAMPLES:

gram meter liter volt

kilogram kilometer kiloliter kilojoule

milligram millimeter milliliter milliamp millisecond

III. THE IMPORTANCE OF PREFIXES•A. FROM MILLI TO KILO

Important prefixes to know:

BASE UNIT DECA 10x

HECTA 100x KILO 1000x

DECI .1CENTI .01

MILLI .001

The base of any defined or

derived unitA 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 1/10 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

Milk

Chocolate

Drinking

Died

Henry

King

BASE UNIT

DECA

HECTA

KILO

DECI

CENTI

MILLICome up

with a sentence to order

the prefixes!

How are we going

to remember

these?

My

Cat

Died

Drinking

Holy

Ketchup

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?

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?

Did you answer 10?Who thinks 50?

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 conversions!!

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…)

BASE UNIT

DECA

HECTA

KILO

DECI

CENTI

MILLITo change to a smaller unit move the decimal to the right and fill in the zero’s

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

Down and to the LEFT

That is…

Up and to the RIGHT

That is…

That is…

Up and to the RIGHT

That is…

Down and to the LEFT

That is…

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:

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

METER

KILOMETER

REMEMBER…

MILLICENTIDECI BASE UNIT DEKAHECTO KILO

54,500

54.500

Use the chart…

MILLICENTIDECI BASE UNIT DEKAHECTO KILO

5450.0545.00

METER

KILOMETER

REMEMBER…

54,500 METERS

= 54.5 KILOMETERS

MILLICENTIDECI BASE UNIT DEKAHECTO KILO

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

To change to a smaller unit,

amps

milliampsMILLICENTIDECI BASE UNIT DEKAHECTO KILO

14.3

14300

Use the chart…

MILLICENTIDECI BASE UNIT DEKAHECTO KILO

1431430

14.3 amps

SAMPLE PROBLEM:

14.3 0 0 .

Converts to:

= 14300 milliamps

SAMPLE PROBLEM:

SAMPLE PROBLEM:

Metric Activity

1. Length of your shoe in mm

2. Your height in dm

3. Width of the hallway in meters

4. Circumference of your head in cm

5. Area of your desk in cm2

Shoe (mm) Height (dm) Hallway (m) Head (cm) Desk (cm2)

290 180 3 55 7830

315 7.5 2.7 51 8056

320 17.2 3 58.5 8056

290 17 2.99 57 8056

330 18.4 3.3 63 17,422.5

300 17.6 3.3 60 17,422.5

240 12.1 2.69 57 7830

270 14.9 2.67 51.5 8,258.25

270 15.3 2.7 54 7830

3000 1600 2.5 460 16100

220 15.7 2.31 51 8056

25 1560 2.7 58 16695

248 1400 2.7 54 78.3000

301 16.9 2.99 50 8056

310 18 2.99 55 8056

260 165 2.99 50 16100

260 164 2.99 51 15812

270 163 3.1 54.5 15812

210 15.5 3 54 95.6

Now find...

1. Class shoe length in meters

2. Average height in cm

3. Average head size in dm

Shoe (mm) Height (dm) Hallway (m) Head (cm) Desk (cm2)

225 14.85 3.055 54 16,192

325 17.4 3.01 56.3 16,192

250 15.8 3.06 55 14,352

320 18.8 3.08 57.5 8082.5

250 15.5 3.02 48 14,352

300 17.8 3.01 56 1620

320 16.2 3.5 57 7750

240 15.0 3.08 55 8082.5

320 17 3.5 55 7750

250 16.2 3.1 58.5 7,705

1. Class shoe length in meters

2. Average height in cm

3. Average head size in dm

SAMPLE PROBLEM:

Sometimes numbers can still be quite large or quite small

For this scientists use scientific notation

65,000,000,000,000 km

.0000000000001 mm

Scientific Notation

The number must be expressed so only a single digit remains to either the right or left of the decimal point

65,000 = 6.5 x10 4

Scientific Notation

The power of 10 is the number of places the decimal place must be shifted

65,000 = 6.5 x10 4

Scientific Notation

If the decimal point is shifted left the exponent is positive

65,000 = 6.5 x10 4

Scientific Notation

If the decimal point is shifted right the exponent is negative

0.0001 = 1.0 x10 -4

Scientific Notation

0.007 = 7.0 x 10

4,500,000 = 4.5 x 10

167,000 =

.000046 =

6?

?-3

1.67 x 105

4.6 x 10-5