H. E. Smith 
Physics 11  The Units of Science 
Introduction
It's always a good idea when you're traveling, to try and learn a few
words of the local language. So, as you set out to explore the physical
world, let me introduce you to a few words, units and "currency" that
you'll encounter on the trip.
Scientific Notation
The important numbers in Physics span almost 40 orders of magnitude in size.
Consider the mass of the Sun:
It's cumbersome, to say the least, having to write out all of those zeros.
Even changing the units to metric tons (eliminate 3 zeros) doesn't
help much. Furthermore, we really don't know the Sun's mass beyond the
accuracy of the fourth digit. All those zeros are just placekeepers,
carrying no useful information.
For this reason, scientists use a shorthand called
scientific notation
to express very large or very small numbers.
In scientific notation the Sun's mass becomes:

The number above the ten, called the power of ten or exponent,
stands for the number of decimal places. If it is positive, as in the mass of
the Sun, the decimal places are in front of the decimal point. So,
10^{30} means
"move the decimal point 30 places to the right and fill the empty
places with zeros" (or, more mathematically, multiply by ten 30 times).
For very small numbers, such as the mass of the proton, we use negative powers
of 10.
For negative exponents, the powers of 10 are after the decimal point; 10^{27} means "move the decimal point 27 places to the left and fill in with zeros" (or divide by ten 27 times).
There are several good web pages about Scientific Notation. If you would like to read a bit more, try out the University of Maryland's Astronomy Programs site, with a Scientific Notation Exercise and an Astronomical Distance Calculator.
Arithmetic with scientific notation is just two easy steps, as shown in the tables below.
Multiplication  

Step 1: Multiply numbers  
Step 2: Add exponents 
So:
Addition / Subtraction  

Step 1: Convert to a common exponent  
Step 2: Add or subtract. 
The Milky Way Galaxy  count the stars if you have a bit of free time.
The mass of the sun, a typical star is about 2 x 10^{30}
kilograms. (Your mass is about 70 kgs!)
Then, the mass of the Milky Way is the number of stars times the mass of a
typical star:
So that:
This is, of course, a crude estimate, especially because we now know that the mass of the Milky Way is dominated by unseen matter.
Division in Scientific Notation is just the inverse process:
Division  

Step 1: Divide numbers  
Step 2: Subtract exponents 
Another example will show how it's done. Suppose you wanted to estimate the number hydrogen atoms in the sun. One estimate would be to divide the sun's mass by the mass of a hydrogen atom. (This assumes that the Sun is composed entirely of hydrogen atoms. It is mostly hydrogen, with some helium and other heavier elements thrown in.)
Metric Prefixes  

PREFIX  DEFINITION  SCIENTIFIC NOTATION 
PREFIX  DEFINITION  SCIENTIFIC NOTATION 
tera  1,000,000,000,000  10^{12}  centi  .01  10^{2} 
giga  1,000,000,000  10^{9}  milli  .001  10^{3} 
mega  1,000,000  10^{6}  micro  .000001  10^{6} 
kilo  1,000  10^{3}  nano  .000000001  10^{9} 
deka  10  10^{1}  pico  .000000000001  10^{12} 
deci  .1  10^{1}  femto  .000000000000001  10^{15} 
Here is a list of prefixes from the National Institute of Standards and Techonology (NIST).
A few examples of how to use the metric prefixes:
Even the "world standard" metric system has different versions.
Astronomers use a version
of the cgs (CentimeterGramSecond)
system,
modified for the immense distances in the Universe and huge masses of
astronomical objects. Most physicists are converging on use of the MKS
(MeterKilogramSecond) version or Systeme Internationale (SI).
To describe distances and sizes, we define a standard of length.
The SI unit of length is the meter, abbreviated
"m". A meter is a little longer than a yard (39.37 inches)
There are three special units of distance used by astronomers. These
are the astronomical unit (AU), the
lightyear and the
parsec. The astronomical unit is the average distance of the Earth
from the Sun shown above.
A lightyear (ly) sounds like a measure
of time, but it is a length  the distance light travels in one year.(We
can use a lightyear as a unit of measure because ALL light travels at the
same speed; it is a fundamental constant of the Universe. More about this
later...) So, in one year, light travels:
The name parsec comes from the technique of measuring distance called
parallax. The nearest star, Alpha Centauri, is about 1.3 pc or
4 lightyears away.
In addition to these distance units, astronomers use the
Ångstrom(Å) as a measure of size on the atomic scale.
Everyone knows that the astronauts weigh less when they're walking on the Moon than when they're back on Earth. Since the Moon is less massive than the Earth, it's gravitational attraction is smaller. It is essential to have a unit for measuring "amount of stuff" that would be the same everywhere in the Universe. That unit of "stuff" is called mass. So, an astronaut's weight is less on the Moon, but his/her mass is exactly the same. Actually,weight and mass are two different things. Your weight is the gravitational attraction between you and the Earth. (Or whatever planet you may be visiting.) Your mass is a measure of your inertia, your resistance to changes in motion. Here is a nice explanation of mass.
The SI unit of mass is the kilogram. It is
about 10% over two pounds:
On the very large (astronomical) scale and the very small (atomic) scale two other units of mass are used. To measure atomic masses the atomic mass unit (amu) is employed. the amu is defined as onetwelfth the mass of a common carbon atom:
slightly less than the mass of a proton. For stars, galaxies, etc. we use the solarmass
where the "" is the standard astronomical symbol for the sun. The mass of our Milky Way Galaxy is about 10^{12}M_{}.
The MKS unit of time is the second. The
time standard is kept by the NIST using a cesium atomic clock like the
one to the right.
 Atomic clock at NIST 
Much of physics and astrophysics is concerned with understanding the energy generation and energy output from objects. Energy conservation principles are among the most important and useful physical tools. The SI unit of energy is the joule. A joule is the amount of energy contained in the motion of a 1 kilogram mass moving with a velocity of 1 meter/second or about the energy represented by a brick moving at 2 mph. The energy output, production, or consumption of an object is its Power, measured in joules/second or Watts. A 100watt light bulb consumes 100W of electrical energy. A possibly more familiar unit of power, the horsepower is related by:
At the atomic / nuclear level, energies are often given in
electronvolts (abbreviated as "eV"), the
energy of an electron
accelerated through a voltage of 1 volt (1 eV =
1.6 x 10^{19} joules).
The energylevels and ionization energies of most atoms are a few eV.
Xray photon energies are frequently quoted in
kiloelectronvolts(KeV). Gammarays and nuclear energies are
most often in MeV.
As stated in Einstein's formula,
In nature, forces are the "pushes" that cause
masses to move.
F = ma 
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