Abecedarium Mensurarum
A Grammar of Physical Scales

Learn what it means to add another zero to the end of a number.
Learn how a measurement can be scaled up or down by a factor of ten.
Learn how a measurement can be scaled by any power of ten.
Learn how to make an an order-of-magnitude estimate.


Memorize the following up-scaling prefixes:

deca	bigger by 10 (Decimal)
hecto	bigger by 100
kilo	bigger by 3 powers (kilometer=100m)
mega	bigger by 6 powers (megabucks=$1,000,000)
giga	bigger by 9 powers (giant)
tera	bigger by 12 powers (Twelve, terror)
peta	bigger by 15 powers (Phifteen)
exa	bigger by 18 powers (Eighteen)
zetta	bigger by 21 powers
yotta	bigger by 24 powers (Yolks of 2 dozen eggs)

(Note: suggested mnemonics are in parentheses.)

Memorize the following down-scaling prefixes:

deci	smaller by 10 (Decimal)
centi	smaller by 100 (centimeter=1/100m)
milli	smaller by 3 powers (centimeter=1/1000m)
micro	smaller by 6 powers (microscope required)
nano	smaller by 9 powers (Nine)
pico	smaller by 12 powers (Pack a dozen eggs)
femto	smaller by 15 powers (Fifteen)
atto	smaller by 18 powers (Ate-teen)
zepto	smaller by 21 powers
yocto	smaller by 24 powers (Yolks, again)

Know relation to American number names:
 - hundred = hecto, deci
 - thousand = kilo, milli
 - million = mega, micro
 - billion = giga, nano
 - trillion = tera, pico

Know rough conversions to common measurements:
 - 1m	1 yard (+ 3 in)
 - 1km	6/10 mile
 - 1cm	4/10 inch

Know astronomical lengths:
 - 1AU	150 millon km
 - 1LY	10 trillion km (actually 9.5, not 10)

Memorize an object or two for each of the following size scales:

1	human body
10	my house
100	sports field, Great Pyramid
^3	my neighborhood (mile)
^4	Mt. Everest
^5	Bay Area (large city)
^6	California (large state), Ceres
^6.5	Moon
^7	Earth, Jupiter's Great Red Spot
^7.5	high satellite orbit
^8	Jupiter
^8.5	a light-second
^9	Moon orbit, Sun
^10	a few days (4) of Earth orbit
^11	Earth orbit (1 AU)
^12	Jupiter orbit (5 AU), Betelgeuse
^13	Solar System
^14	Heliopause
^15	(empty space around Sun)
^16	a light year, Oort cloud
^16.5	nearest stars (Proxima Centauri, Sirius)
^17	Crab Nebula (size of)
^18	globular cluster (M13)
^19	DISTANCE to Orion Nebula
^20	Small Magellanic Cloud (size of)
^21	Milky Way Galaxy (diameter)
^22	DISTANCE to Andromeda Galaxy
^23	DISTANCE to Virgo Cluster
^24	Local Supercluster (diameter)
^25	(empty space around supercluster), 1 billion LY
^26	known universe

.1	human hand
.01	human fingertip
^-3	pencil tip, ant (millimeter)
^-4	dust mite, paramecium, human hair
^-5	cloud droplet, human cell
^-6	bacterium, red light wave (micron)
^-7	chromosome, smoke particle
^-8	THICKNESS of flagellum
^-9	THICKNESS of DNA helix
^-10	atom, X-ray wave (angstrom)
^-12	gamma ray wave
^-14	nucleus of atom
^-15	proton
^-18	quark, electron ("point particles")
^-35	Planck length (smallest possible distance)

Know microscopic lengths:
 - micron	millionth of a meter
 - angstrom	10^-10, 1/10,000 micro

Learn to compare objects as a difference in order:
 - The Earth is 7 orders larger than me.
 - The Earth is 9 orders larger than my fingertip.
 - I am 10 orders larger than an atom.
 - The Earth is 17 orders larger than an atom.
 - A cell is 6 orders smaller than me, like I am to California.

Learn how flat, 2d area scales at twice the power of length:
 - A million square millimeters in a square yard.
 - A million square meters in a square kilometer.
 - Estimate 1 square meter (OOM) on meter-sized disk or sphere.
 - Estimate 10^8 square kilometer (OOM) of Earth's surface.

Learn how solid, 3d volume scales at thrice the power of length:
 - A million cubic centimeters in a cubic meter.
 - A billion cubic millimeters in a cubic meter.
 - A billion cubic meters in a cubic kilometer.
 - About a trillion cubic kilometers in the earth.

Learn which instruments observe which scales:
 - Telescope (out to nearby galaxies)
 - Microscope (down to a cell)
 - Electron microscope (cell parts)

Electromagnetic spectrum orders
 - radio: 10 centimeters and larger
 - microwave: 10 centimeters to 1 millimeter
 - visible light: 4/10-8/10 micron (red is longest)
 - X-rays: 1/10-100 angstroms
 - gamma rays: 1/100 angstrom or less

Links:
 http://powersoften.com/
 http://en.wikipedia.org/wiki/Orders_of_magnitude
 http://en.wikipedia.org/wiki/Electromagnetic_spectrum
 http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html