 # UNDERSTANDING AND USING THE METRIC SYSTEM

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UNDERSTANDING AND USING THE METRIC SYSTEM

INTERNATIONAL STANDARDS EASE OF RECORDING C. EASE OF CALCULATIONS
I. ADVANTAGES OF THE METRIC SYSTEM FOR SCIENCE INTERNATIONAL STANDARDS EASE OF RECORDING C. 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
A. INTERNATIONAL STANDARDS… * * All metric system units are based on specific definitions which are internationally known standards and are reproducible Volume =1.0 liter *THAT IS, MEASUREMENTS ARE THE SAME ALL OVER THE WORLD… REGARDLESS OF COUNTRY OR LANGUAGE Length =1.0 meter Mass = 1.0 kilogram

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 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: 2.351 liters .802 meters 5.45 centimeters 9.023 meters 5.613 grams

This is a huge advantage over the older “fraction” based systems…
Recording measurements is too complex, prone to errors… 1/12 unit 1/16 unit 1/2 unit Examples: 2 miles, 235 yards, 2 feet, 7 inches 2 pounds, 8 9/32 ounce 4 gallons, 1 quart, 5 ¾ ounces 5 yards, 2 feet, 7 1/16 inch

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.1ft 1½ in)

II.UNITS OF MEASUREMENT

II.UNITS OF MEASUREMENT
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
THE “BASE” UNITS: #2 1 DECIMETER 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 liter = 1dm3 1 DECIMETER

II.UNITS OF MEASUREMENT
#3 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

II.UNITS OF MEASUREMENT
#4 THE “BASE” UNITS: The unit of TIME: the SECOND…

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: milligram millimeter milliliter milliamp millisecond gram meter liter volt kilogram kilometer kiloliter kilojoule

III. THE IMPORTANCE OF PREFIXES
A. FROM MILLI TO KILO This prefix changes the base into a unit 1/100 as large as the base The base of any defined or derived unit This prefix changes the base into a unit 1/1000 as large as the base Important prefixes to know: This prefix changes the base into a unit 1/10 as large as the base A prefix that makes a unit 10x larger than the base MILLI .001 CENTI .01 This prefix changes the base into a unit 100x larger DECI .1 This prefix changes the base into a unit 1000x larger BASE UNIT DECA 10x HECTA 100x KILO 1000x

Come up with a sentence to order the prefixes!
Milk Chocolate Drinking Died Henry King MILLI My Cat Died Drinking Holy Ketchup Come up with a sentence to order the prefixes! CENTI How are we going to remember these? DECI BASE UNIT DECA HECTA KILO

Understanding prefixes…
Let this entire box represent 1.0 liter… 1/10th (.1) of the box could be called a ‘deciliter How many of these would be in 1 liter? 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? To get those values, did you just multiply by 10? In 5 liter? Did you answer 10? Who thinks 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 conversions!! 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? How many of these are in the 1.0 liter? What did you do to get that answer? 1000? Milliliter?? 1. = 1000 ml

To 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 MILLI CENTI DECI BASE UNIT DECA HECTA KILO

That is… That is… Up and to the RIGHT Down and to the LEFT

That is… That is… Up and to the RIGHT

That is… Down and to the LEFT

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’

MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
To change to a larger unit move the decimal to the left and fill in the zero’s REMEMBER… MILLI CENTI DECI BASE UNIT DEKA HECTO KILO METER KILOMETER

MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
Use the chart… MILLI CENTI DECI BASE UNIT DEKA HECTO KILO 54,500 5450.0 545.00 54.500

MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
REMEMBER… MILLI CENTI DECI BASE UNIT DEKA HECTO KILO METER KILOMETER 54,500 METERS = 54.5 KILOMETERS

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:

MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
milliamps amps To change to a smaller unit, move the decimal to the right and fill in the zero’s

MILLI CENTI DECI BASE UNIT DEKA HECTO KILO
Use the chart… MILLI CENTI DECI BASE UNIT DEKA HECTO KILO 14300 1430 143 14.3

SAMPLE PROBLEM: 14.3 amps Converts to: . 14.3 = 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 58.5 17 2.99 57 330 18.4 3.3 63 17,422.5 300 17.6 60 240 12.1 2.69 270 14.9 2.67 51.5 8,258.25 15.3 54 3000 1600 2.5 460 16100 220 15.7 2.31 25 1560 58 16695 248 1400 301 16.9 50 310 18 260 165 164 15812 163 3.1 54.5 210 15.5 95.6

Now find... 1. Class shoe length in meters 2. Average height in cm
3. Average head size in dm

1. Class shoe length in meters 2. Average height in cm
Shoe (mm) Height (dm) Hallway (m) Head (cm) Desk (cm2) 225 14.85 3.055 54 16,192 325 17.4 3.01 56.3 250 15.8 3.06 55 14,352 320 18.8 3.08 57.5 8082.5 15.5 3.02 48 300 17.8 56 1620 16.2 3.5 57 7750 240 15.0 17 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:

65,000,000,000,000 km Sometimes numbers can still be quite large or quite small For this scientists use scientific notation mm

65,000 = 6.5 x10 4 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

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

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

0.0001 = 1.0 x10 -4 Scientific Notation
If the decimal point is shifted right the exponent is negative = 1.0 x10 -4

Scientific Notation -3 ? 0.007 = 7.0 x 10 4,500,000 = 4.5 x 10 6 ? 167,000 = = 1.67 x 105 4.6 x 10-5