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Reference Guide

Metric System - Reference Guides

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Department
Basic Engineering
Course Code
BE 1101
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All

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Metric System
Metric System
INT R ODU C TIO N SU PPL E MEN TARY U N IT S
LEN G TH ( m)
The International System of Units (SI) is a
modern version of the metric system
• As a result of a long series of international
discussions, on the 14th of October, 1960,
the Eleventh General Conference on Weights
and Measures agreed to adopt the symbol SI
(Le Systéme International d’Unités) to
describe system of measurements consisting
of seven basic units, two supplementary
units, and numerous derived units
• These units appear on this chart along with
their definitions
• Multiples and submultiples are expressed in
the decimal system
• SI has only one unit for any physical quantity
and therefore no conversion factors or
constants need to be remembered
• Radian and steradian are often listed as
supplementary units; the current international
agreement puts these two dimensionless units
into the derived unit category
• The radian (rad) is the plane angle formed
between 2 radii of a circle subtended by an arc
whose length is equal to radius; there are 2p
rad in a circle
• The steradian (sr) is the solid angle at the
center of a sphere which subtends an area on
the sphere’s surface which is equal to the
square of its radius; there are 4psr in a sphere
• The SI system still permits the use
of degrees (deg,°), where 1 circle = 360°
• The use of minutes and seconds is
discouraged; decimal divisions of a degree
should be used
THE RADIAN (rad)
THE STERADIAN (sr)
surface area
= 1 r2
1 rad
2 rad
3 rad
solid angle
1 sr
1 rad
π rad
π = 3.1416
• The SI unit of length is the meter (m)
• Originally, it was 1 ¥107of the
longitude passing through Paris from the
equator to the North Pole
123456789
10
1 2 3 4 5 6 7 8 9
20
123456789
30
12 3 4 5 6 7 8 910111213 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
123456789
40
123456789
50
1 2 3 4 5 6 7 8 9
60
1 2 3 4 5 6 7 8 9
70
1 2 3 4 5 6 7 8 9
80
123456789
90
1 2 3 4 5 6 7 8 9
100
1 millimeter (mm)
1000 mm = 1 m
1 centimeter (cm)
1cm = 10 mm
100 cm = 1 m
1 decimeter (dm)
1dm = 10 cm
1 dm = 100 mm
10 dm = 1 m
1 foot = 30.48 cm
1 yard = 3 ft = 0.9144 m
1 m = 3.2808 ft = 39.3701 in
METER
YARD
KRYPTON 86
(LAMP)
1 650 763.73 wavelengths
1 meter
* Orange-red line of the spectrum of Kr-86
2p10 to 5d5 transition*
• The most commonly
used derivatives of the
meter are area (m2)
and volume (m3)
• The diagrams show
how m, m2, and m3,
as well as their
multiples and sub -
multiples, relate to
objects in everyday life
1 m
Long Step
1 dm
Hand Width
1 cm
Smallest Finger
(Nail Width)
1 mm
Dime Thickness
A
1 m2
Desk Top
1 dm2
Palm
1 cm2
Nail on
Smallest Finger
1 mm2
Thumbtack
Hole
MILK
1 m3
Trunk of
Station Wagon
1 dm3
Quart of Milk
1 cm3
( )
1 cm3
Baby Spoon
1 mm3
Pin Head
1 cm3 = 0.061 in3
1 dm3 (liter) = 1000 cm3 = 0.001 m3
• The standard meter is currently defined as the length of 1,650,763.73 wavelengths (in a vacuum)
of radiation corresponding to the unperturbed transition between the energy levels 2p10 and 5d5
of the Krypton-86 atom
• The wavelength of this orange-red line is 6.057 802 ¥10–7 m
LENGTH (M)
VOLUME (M3)AREA (M2)
1METRIC SYSTEM 1-55080-859-1
l e a r n r e f e r e n c e r e v i e w
TM
permacharts
© 1996-2013 Mindsource Technologies Inc.
w w w . p e r m a c h a r t s . c o m

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Description
l e a r n • r e f e r e n c e • r e v i e w permacharts TM Metric System Metric System INTRODUCTION S UPPLEMENTARY UNITS 2 rad • The International System of Units (SI) is a • Radian and steradian are often listed as modern version of the metric system supplementary units; the current international 3 rad agreement puts these two dimensionless units • As a result of a long series of international discussions, on the 14th of October, 1960, into the derived unit category π rad 1 rad the Eleventh General Conference on Weights • The radian (rad) is the plane angle formed π = 3.1416 and Measures agreed to adopt the symbol SI between 2 radii of a circle subtended by an arc (Le Systéme International d’Unités) to whose length is equal to radius; there are 2p describe system of measurements consisting rad in a circle THE RADIAN (rad) of seven basic units, two supplementary • The steradian (sr) is the solid angle at the units, and numerous derived units center of a sphere which subtends an area on surface area • These units appear on this chart along with the sphere’s surface which is equal to the = 1 r2 their definitions square of its radius; there are 4p sr in a sphere solid angle 1 sr • Multiples and submultiples are expressed in • The SI system still permits the use the decimal system of degrees (deg,°), where 1 circle = 360° 1 rad • SI has only one unit for any physical quantity • The use of minutes and seconds is and therefore no conversion factors or discouraged; decimal divisions of a degree constants need to be remembered should be used THE STERADIAN (sr) LENGTH (m) • The SI unit of length is the meter (m) • The standard meter is currently defined as the length of 1,650,763.73 wavelengths (in a vacuum) –7 of radiation corresponding to the unperturbed transition between the energy levels 2p and 5d • Originally, it was 1 ¥ 10 of the 10 5 longitude passing through Paris from the of the Krypton-86 atom equator to the North Pole • The wavelength of this orange-red line is 6.057 802 ¥ 10 –7 m 1 decimeter (dm) 1 centimeter (cm) 1dm = 10 cm 1 millimeter (mm) 1cm = 10 mm 1 m = 3.2808 ft = 39.3701 in 100 cm = 1 m 1 dm = 100 mm 1000 mm = 1 m 10 dm = 1 m 1 23 4 5 6 7 8 9101 2 3 4 5 67 8 9 2 1 23 4 5 6 7 8 9301 2 3 4 5 67 8 9 4 1 2 34 5 6 7 8 9501 2 3 4 5 6 78 9 601 2 34 5 6 7 8 9701 2 3 4 5 6 78 9 801 2 3 45 6 7 8 990 12 3 4 5 6 78 9100 METER 1 yard = 3 ft = 0.9144 m 1 foot = 30.48 cm 1 2 34 5 6 7 8 9 0 11 211 3 4 6 1517 119810 21 22 23 24 2 5 6 8 2 729 3 132 33 3 435 36 3 YARD 1 650 763.73 wavelengths LENGTH (M) 2p to 5d transition* • The most commonly 10 5 used derivatives of the 2 1 m 1 dm 1 cm 1 mm meter are area (m ) 3 and volume (m ) • The diagrams show how m, m , and m , 3 as well as their 1 meter multiples and sub- KRYPTON 86 Long Step Hand Width Smallest Finger Dime Thickness multiples, relate to (Nail Width) (LAMP) objects in everyday life A * Orange-red line of the spectrum of Kr-86 2 2 2 3 1 m 3 1 dm 3 1 cm 3 AREA (M ) 1 m 1 dm VOLUME (M ) 1 cm = 0.1655 in 2 3 3 1 cm = 0.061 in M IK Trunk of Desk Top Palm Station Wagon Quart of Milk ( ) 3 3 1 cm 2 1 mm 2 1 cm 1 mm 1 dm 2 = 100 cm = 0.01 m 2 3 3 3 1 dm (liter) = 1000 cm = 0.001 m Nail on Thumbtack Smallest Finger Hole Baby Spoon Pin Head 1 METRIC SYSTEM • 1-55080-859-1 www.permacharts .com © 1996-2013 Mindsource Technologies Inc. l e a r n • r e f e r e n c e • r e v i e w permachartsTM TEMPERATURE (K) Freezing WaterHuman Body Boiling Water • The SI unit of thermodynamic temperature is the kelvin (K), which is 0 233.15 273.15 310 373.15 defined as the fraction 1/273.15 of the thermodynamic temperature of the K triple point of pure water KELVIN 0 -40 0 36.9 100 • Ordinary temperature measurements are made with the Celsius scale, on T C which the freezing point of pure water is zero degrees Celsius (0ºC) L–273.15 CELSIUS S -40 32 98.4 212 0 • The degree symbol (º) is always associated with the Celsius scale, but not B–459.67 F with Kelvin A FAHRENHEIT MASS (kg) LUMINOUS INTENSITY (cd) • The SI unit of mass is kilogram (kg) • The candela (cd) 1CANDELA • It is the only SI base unit that is the SI unit for incorporates a multiplying prefix 317,515 kg measuring 2 700,000 lb 10/6 mm (kilo) luminous • The kilogram is nearly equal to the intensity INSULATION –3 3 FREEZING mass of a liter (10 m ) of pure 1 kg = 2.205 lb 1 lb = 0.4536 kg 1 oz = 28.35 g • It is defined as PLATINUM water at 4°C the luminous 2045 K • It is defined in terms of the mass of intensity, 1000 kg 1 kg 1 g 1 mg perpendicular to 100 watt bulb has the International Prototype a luminous intensity of Kilogram made of platinum-iridium KLI the surface of2 approximately 135 cd alloy and stored at Sèvres, France, M 1/600 000 m in the custody of the International Small Car Large Carrot area, of a perfect “black body” at the temperature QuMilkof Thumbtack Seed of freezing platinum (2045 K) under a pressure of Bureau of Weights and Measures 2 101 325 newton/m TIME (s) PREFIXES • The second (s) 9 192 631 770 cycles • Multiples of SI units are named by adding a prefix to is the SI meter, gram, watt, and so on unit of time • Abbreviations use the appropriate prefix letter (such • The second is 1 second as, ns for nanosecond, kHz for kilohertz) defined • For extremely large or small numbers, use as the time duration yotta (Y) =10 , zetta (Z) =10 , zepto (z) =10 –21, of 9,192,631,770 –24 periods of the radiation of the transition between and yocto (y) =10 18 the two hyperfine levels of the ground state of the Cesium-133 atom exa E 10 one quintillion • Despite attempts to use the powers-of-ten multipliers for long periods of peta P 10 15 one quadrillion time, the minute (min), hour (h), day, week, and year are still tera T 10 12 one trillion commonly used and acceptable international time units 9 giga G 10 one billion mega M 10 6 one million kilo k 10 3 one thousand 2 hecto h 10 one hundred QUANTITY OF MATTER (mol) deca da 10 1 ten • The SI unit of the amount of substance or quantity of 10 0 one matter is the mole (mol) –1 • It is defined as the amount of a substance of a deci d 10 one tenth centi c 10 –2 one hundredth system which contains as many elementary units as there are carbon atoms in 0.012 kilograms milli m 10 –3 one thousandth (12 grams) of carbon-12 –6 micro µ 10 one millionth • The elementary unit or entity must be specified nano n 10 –9 one billionth and may be an atom, molecule, ion, electron, a
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