Units of Length, Area, and Volume
|To make life easier for everybody, the choice of units was taken away from you and me, not to mention your local Lords, Archdukes or Kings, more than 100 years ago, and given to scientists. As a result, everybody is now required to adhere strictly to the international standard system or SI units. Of course, the SI units are based on the metric system.|
|The SI system basically knows only seven basic units. Here they are:|
|Let's forget about the "Luminous
intensity" right away, and refer "Amount of substance" and "Thermodynamic temperature
" to their links. |
Time is not a problem because seconds, minutes, hours etc. are rather well known to all of us (and still non-metric!).
Those of us who know what an electrical current is, know about Ampere (A) and I need not explain. If you personally are not always 100 % sure if it should be Ampere (A) or Volt (V), you don't know a thing about electricity and I needn't explain either.
Mass is not too difficult either. In case of doubt you can go far with remembering that 1 kg are roughly 2 pounds.
That leaves us with length and the general issue of how to deal with very small or very large numbers.
|In this Hyperscript we need to deal with very small lengths. But for good measure, I also throw in very large lengths.|
|We deal with very small or very large numbers in
two way. First and best by using "exponentials",
i.e. by giving the potency of 10. The potency is the exponent
or the small raised number to the right of the "10". It simply gives the number
of zeros that you would have to write in the good, old-fashioned way
|Second, we assign special names and abbreviations of those names to (mostly) orders of thousands. For example: "kilo" = thousand, "mega" = Million. For small numbers it's for example "micro" = millionth, or "nano" = billionth (american kind).|
|Heres is the list. Besides numbers some (small) relations are also given. The most common one is the percent (%), but there are more, always called "parts per...".|
|We shall be quite interested in the nanometer (nm), the billionth part of a meter, or |
nanometer is not a lot. Let's get a feeling for what it
implies by looking at some small things you might relate to: |
|No let's see how we count if we don't use the scientific abbreviations like mega = million|
|For some odd reason, different cultures count differently whenever they get to large numbers:|
|Beware! Confusion about billions or trillions is guaranteed, in particular
because the British switched to the American way of counting. Of course the German way is
the better way. Just look at your countries public debt. 5 Billion sounds just far friendlier
than 5 Trillion.
The present American debt thus amounts to: 14 trillionUS $, 14 billionGer $, 14 Tera $ (= 14 T$) or
|Conversion from Enlightened to Benighted and Back|
|It remains to look at conversions from the
enlightened decimal SI units to the outdated and benighted US units. Scientists like me and
a lot of other smart people use the SI system because it is a hell of a lot easier than old
non-metric systems. Most people simply comply with the SI system (which was not always the
case) because their governments long ago had signed the international treaty demanding the
introduction of the SI system. |
The Americans, however, prefer to do things the difficult way. They have staunch allies in this: Myanmar (formerly known as Burma) and Liberia. The rest of the world is metric.
Note that measuring temperature in degree Celsius or Fahrenheit is essentially a matter of taste. Not using a non-metric or better non-decimal system for measuring length (and then automatically also area and volume) and weight is a matter of being stubborn or just plain stupid. Sorry, but that's the truth.
I wonder if you know one of the reason why the Americans are still hanging on to their illogical middle-age units (besides general stupidity related to the deplorable level of general education, and an unshakable believe that things as they are in the USA cannot possibly be improved upon). No? Then try this link. You will be amazed.
|Now let's be
a bit self-critical. All of us still use the ancient system for measuring time (and angles)
that's not decimal but sexagesimal (base 60). It originated
with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians,
and it is still used in a modified form for measuring time, angles, and the
geographic coordinates in our modern times. |
So we aren't completely metric either. But at least the ancient Sumerians had a system.
|There is no real system or any justification for inch, foot, yards, miles, acres, pints, gallons, ounces, pound, and so on, except that you can use it for a good one-liner:|
|There is no easy way to convert from the SI metric system to the American non-metric non-system. You need to convert bit by bit. You could commit the rules to memory provided you have nothing better to do, like watching paint dry.|
|Use this table but be careful. I give no guarantee!|
The Pyramid Inch
History of Carbon
Overview of Major Steels: Scientific Steels
Numbers and Concentration
4.1.2 Metals are Crystal
Overview of Major Steels
7.1.1 Finding Your Way in the Iron Carbon Phase Diagram
Discovery of Atoms
2.1.1 Bang it!
9.2.2 Designing Low Alloy Steels
3.1.1 Breaking Things in Style
4.4.2 Moving Atoms Around
Phenomenological Modelling of Diffusion
Segregation in Silicon
6.1.1 It Takes Two to Tango
Beer and Conquering The World
Overview of Major Steels
Needle Scanning Microscopes
Microscopes for Science
Scanning Electron Microscope
5.4.1 The dislocation
© H. Föll (Iron, Steel and Swords script)