The Metric System

 

Important dates in the history of the modern metric system (S.I.):

1670  metric system originated on about this date. Gabriel Mouton, a French vicar

1790  Thomas Jefferson proposed a decimal-based measurement system for the United States.

1792  The U.S. Mint was formed to produce the world's first decimal currency (the U.S. dollar consisting of 100 cents).

1866  The use of the metric system made legal (but not mandatory) in the United States by the Metric Act of 1866 (Public Law 39-183).  This law also made it unlawful to refuse to trade or deal in metric quantities.

1975  The Metric Conversion Act of 1975 (Public Law 94-168) passed by Congress. The Act established the U.S. Metric Board to coordinate and plan the increasing use and voluntary conversion to the metric system. However, the Act was devoid of any target dates for metric conversion.

1979  BATF requires wine producers and importers to switch to metric bottles in seven standard [liter and milliliter] sizes.

1983  The meter is redefined in terms of the speed of light by the 17th CGPM, resulting in better precision but keeping its length the same.

1988  The Omnibus Trade and Competitiveness Act of 1988 amended and strengthened the Metric Conversion Act of 1975, designating the SI metric system as the preferred measurement system, and requiring each federal agency to be metric by the end of fiscal year 1992.

1991  President George Bush signed Executive Order 12770, Metric Usage in Federal Government Programs directing all executive departments and federal agencies implement the use of the metric system. The Executive Order is also available as an appendix to: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy

1994  The Fair Packaging and Labeling Act (FPLA) was amended by the Food and Drug and Administration (FDA) to require the use of dual units (inch-pound AND metric) on all consumer products.

1996  As of July 1996 all surface temperature observations in National Weather Service METAR/TAF reports are now transmitted in degrees Celsius.

2001 April 09  U.S. Stock Exchanges changed to decimal trading. The Securities and Exchange Commission has ordered that all stocks must be quoted in dollars and cents rather than fractions by this date. The switch to decimal trading brought the U.S. in line with the rest of the world's major exchanges. This follows the change of the Canadian Stock Exchanges to decimal trading in 1996.


One of the principal advantages of the Metric System is its use of only one unit (standard of size) for each parameter (thing that is being measured). The metric units are interrelated in such a way that only seven fundamental standards are necessary. These fundamental standards are identified with an * in the tables below.

The 7 Standard Metric Units

Second - time
kilogram - mass
degrees kelvin - temperature
meter - distance

candle (candela) - light

ampere - current and resistance

mole - amount of substance

MECHANICS

Parameter:

Metric Unit

English Units

time
duration, delay

second *
s

second, minute
hour, day

frequency

Hertz
1/s

cycle per second

length
distance, displacement

meter
1/299 792 458 light sec
m

inch, foot, yard
rod, chain, furlong, mile

velocity, speed
rate of change of position

meter per second
m/s

foot per second
mile per hour, knot

acceleration
rate of change of velocity

meter per second squared
m/s2

foot per second squared

mass
quantity of material

kilogram *
kg

ounce, pound, ton

force
push, pull, or weight

newton
kg m/s2

pound-force

impulse
force times time

newton second
kg m/s

pound-force second

momentum
mass times velocity

kilogram meter per second
kg m/s

pound foot per second

work, energy
force times distance

joule (pronounced "jewel")
= one newton meter
kg m2/s2

foot pound-force

power
rate of doing work

watt
= one joule per second
kg m2/s3

foot pound-force per second
horsepower

area
size of a surface

square meter
m2

square foot, square yard
acre, square mile

pressure
force per unit area

pascal
newton per square meter
kg/m s2

pound-force per square inch

volume, capacity

cubic meter (stere)
m3

pint, quart, gallon
cubic foot, cubic yard

density, heaviness

grams per cubic centimeter
g/cm3

pounds per cubic foot

 


HEAT

Parameter:

Metric Heat Unit

English Heat Unit

heat energy

joule, calorie, Calorie
1 cal = 4.186 joules
1 Cal = 4186 joules

British Thermal Unit

temperature change

kelvin *

Fahrenheit degree

temperature

kelvin

degrees Fahrenheit

 


LIGHT

Parameter:

Metric Light Unit

luminous intensity

candle *

luminous flux

lumen
one candle produces 4 pi lumens

illumination

lux
lumen per square meter

focus

diopter
reciprocal meters

 


ELECTRICITY & MAGNETISM (There are no English electrical units)

Parameter:

Metric Electrical Unit

electric charge

coulomb
96,500 coul = 1 faraday
faraday = 1 mole of electrons

electromotive force (EMF)

volt (joule per coulomb)

capacitance

farad (coulomb per volt)

electric current

ampere (coulomb per second)

electric energy

joule (watt second)
(newton meter)
KWH = 3,600,000 joules

electric power

watt (joule per second)

electrical resistance

ohm   (volt per ampere)

electrical conductivity

siemens (coulomb per joule)
(ampere per volt)

electrical field strength

volts per meter

electromagnetic inductance

henry (pl. henrys)

magnetic field intensity

oersted (formerly the gauss)

magnetic flux

weber (108 maxwells)

magnetic flux density

tesla  weber per square meter

magnetomotive force

gilbert


Each physical quantity (length, mass, volume, etc.) is represented by a specific SI unit. That unit is made larger or smaller by addition of a prefix to the stem unit.


Commonly used metric system units and symbols:

Type of Measurement

Unit Name

Symbol

length, width, distance, thickness, girth, etc.

meter

m

mass (often called weight)

kilogram*

kg

mass (larger)

metric ton

t

time

second

s

temperature

degree Celsius**

C

area

square meter

m2

area (land)

hectare

ha

volume (liquid or other)

liter

L***

volume (larger)

cubic meter

m3

density

kilogram per cubic meter

kg/m3

velocity

meter per second

m/s

velocity (autos)

kilometer per hour

km/h

force

newton

N

pressure, stress

kilopascal

kPa

energy

kilojoule

kJ

power

watt

W


*The gram (g) is the stem unit to which other prefixes are added.
**The kelvin (K) is the SI base unit of thermodynamic temperature.
***The capital el (L) is preferred as the symbol for liter in the USA; however the lower case el (l) also is correct and is used in many metric countries.


Derived Units

Force

newton

N

kg m s-2

Energy

joule

J

kg m2 s-2

Power

watt

W

kg m2 s-3

Frequency

hertz

Hz

s-1

Charge

coulomb

C

A s

Capacitance

farad

F

C2 s2 kg-1 m-2

Magnetic Induction

tesla

T

kg A-1 s-2

 


The Metric Prefixes

 

Prefix:

Symbol:

Magnitude:

Meaning (multiply by):

Yotta-

Y

1024

1 000 000 000 000 000 000 000 000

Zetta-

Z

1021

1 000 000 000 000 000 000 000

Exa-

E

1018

1 000 000 000 000 000 000

Peta-

P

1015

1 000 000 000 000 000

Tera-

T

1012

1 000 000 000 000

Giga-

G

109

1 000 000 000

Mega-

M

106

1 000 000

myria-

my

104

10 000 (this is now obsolete)

kilo-

k

103

1000

hecto-

h

102

100

deka-

da

10

10

-

-

-

-

deci-

d

10-1

0.1

centi-

c

10-2

0.01

milli-

m

10-3

0.001

micro-

u (mu)

10-6

0.000 001

nano-

n

10-9

0.000 000 001

pico-

p

10-12

0.000 000 000 001

femto-

f

10-15

0.000 000 000 000 001

atto-

a

10-18

0.000 000 000 000 000 001

zepto-

z

10-21

0.000 000 000 000 000 000 001

yocto-

y

10-24

0.000 000 000 000 000 000 000 001

   

Commonly used metric prefixes

Prefix Name

Prefix Symbol

Prefix Value

giga G 1 000 000 000 109

mega

M

1 million or 1 000 000

106

kilo

k

1 thousand or 1000

103

hecto

h

100

102

deka

da

10

10

 

 

 

 

deci

d

1/10 or 0.1

10-1

centi

c

1/100 or 0.01

10-2

milli

m

1/1000 or 0.001

10-3

micro

1/1 000 000 or 0.000 001

10-6

nano

N

1/1 000 000 000 or 0.000 000 001

10-9


Some special relationships:

Legal/official (exact) definitions of inch-pound units as set by U.S. law:

Note: In Canada the inch and the pound are defined identically, but 1 Canadian gallon = 4.546 09 liters.

Approximate conversion factors between inch-pound units and the International System of Units (SI):


Some baseline temperatures in the three temperature scales

temperature

kelvins

degrees celsius

degrees fahrenheit

symbol

K

C

F

boiling point of water

373.15

100.

212.

average human body temperature

 

37.

98.6

average room temperature

 

20. to 25.

68. to 77.

freezing point of water

273.15

0.

32.

absolute zero

0.

-273.15

-459.67


Temperature conversions between the three temperature scales:

kelvin / degree celsius conversions (exact):

degree Fahrenheit / degree celsius conversions (exact):



A degree celsius memory device:

There are several memory aids that can be used to help the novice understand the degree Celsius temperature scale. One such nemoic is:

When it's zero it's freezing,
when it's 10 it's not,
when it's 20 it's warm,
when it's 30 it's hot!

Or, another one to remember:

30's hot
20's nice
10's cold
zero's ice

 

Examples of everyday item equivalences for metric units of length, mass, volume, and temperature

(Drawings excerpted from the book, Quick Guide to the Metric System, by Valerie Antoine, USMA Executive Director)

Length:
1 meter (1 m)

1 meter

1 centimeter (1 cm)

1 centimeter

1 kilometer (1 km)

1 kilometer

Mass:
1 kilogram (1 kg)

1 kilogram

1 gram (1 g)

1 gram

Volume:
1 liter (1 L or 1 l)

1 liter

1 milliliter (1 mL or 1 ml)

1 milliliter

Temperature:
degree celsius (C)

degree Celsius



More detail is available in The SI Brochure at

or at  

 

Learn more about Metric Prefixes

View in PowerPoint View as Web Page
Metric Prefixes.pps Metric Prefixes

 

 

Learn how to convert one unit of measure into another unit of measure  
Factor-Label Examples & Practice Problems

 

Scientific Notation

  Learn how to write numbers in scientific notation

http://www.nyu.edu/pages/mathmol/textbook/scinot.html           

 

More info

http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html    

 

Temperature conversions (C <--> F)

 

Sources:

http://lamar.colostate.edu/~hillger/

http://users.aol.com/tspquinn/units.html

http://www.essex1.com/people/speer/metric.html

http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl         

http://www.nyu.edu/pages/mathmol/textbook/scinot.html           

http://dbhs.wvusd.k12.ca.us/SigFigs/Scientific-Notation.html    

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