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Scientific Notation for Everyman

. . . even scientists.

Scientific notation is a way of expressing very large and very small numbers in a reasonably concise manner. I'm presuming you're familiar with it. (It'd be pretty weird for you to be here reading up on how to improve something you don't even know about!)

Scientific notation is less than ideal for the following reasons: it's cumbersome to say, cumbersome to write, and has always been and still is impossible to type on a keyboard. I can't imagine who thought it up. (Well, I have an idea, but I don't want to set off the inhabitants of a certain European country already famous for their testiness.) It's not the slightest wonder that it never caught on with the masses. Which is a shame.

I argue in my proposal for a fantastically simplified system of units of measure that we would surely gain a better feel for how things in nature compare if we always measured the same property using the same unit - all the way from the size of an atom to the size of a cell to the size of a person to the size of the earth... to the size of the universe.

To do that, we need to be perfectly comfortable with big and small numbers.

To be fair, I should have conceded above that the basic idea of scientific notation is great - using powers of ten in expressing large and small numbers. It's just that the written notation and the spoken words associated with it are a total pain in the neck.

Where there's a problem, I always say, there's a solution. And most of the time the statement of the problem practically cries its own solution.

In this case, all that's needed is a simple character and a simple syllable to stand for the "times ten to the plus" and "times ten to the minus" folderol of scientific notation.

The final decision on clear and efficient characters and syllables can be left to a panel of clever people, but here are some suggestions to get the ball rolling. How about an overscore and an underscore to indicate "times 10 to the (plus)" and "times 10 to the minus", respectively? It would look like this:

          In with the NEW:     4 7       5_6      (Yaaaayyy!!!)

                                   7         -6
          Out with the OLD:    4x10      5x10     (Booooooo...)

If over- and underscores have uses at all, I can't think of what they are or how they might create confusion with this notation. But there certainly may be better ideas for the new symbols.

Next we need a simple syllable for each case of positive and negative powers of ten. For years I've been thinking "bip" for "times ten to the plus", and "bop" for "times ten to the minus". I know that can be improved upon. Sounds like a kid's song. ("I never knew just what it was, and I guess I never will...") I had a brainstorm the other day, but didn't write it down and so it appears to be lost forever. So sad.

          The NEW rap        The OLD song and dance        
          --------------     ---------------------------------- 
          Four bip seven.    Four times ten to the (plus) seven.
          Five bop six.      Five times ten to the minus 6.     

Scientific notation requires the placement of a decimal point after the first digit. For this streamlined notation, perhaps we might feel freer to choose a power of 10 so that the leading factor is a simple one- to three-digit integer, and dispense with the fly specks. Notice how often two digits provide more than enough precision for our needs. Does anybody really care if someone has 6.37 million dollars, as opposed 6.4 (or just 6) million dollars?

In our streamlined scientific notation we can express every number from .000000010 to 99000000000 to two-place precision with four strokes of the pencil or less.

                                 -8         10
          That was THEN:   1.0x10     9.9x10     (Blechhh!) 

          This is NOW:     10_9       99 9       (Ahhhh...)

Pretty impressive, eh? Notice how the old scientific notation represents a savings of a mere 2 characters for the small number, and a mere 3 characters for the large one. Admittedly, it saved us the trouble of counting up the zeros.

That's about all I have to say here; the streamlined notation and talk would bring acceptance of scientific notation to the media and the masses, and the benefits would be substantial. We might have to add a character or two to our keyboards, but that shouldn't hold us up. When we switch over to the simplified system of units of measure, a simple and efficient way of expressing large and small numbers will be mandatory.

Of course, everything here applies just as well to other number systems, looking ahead to when we switch from clumsy old Base 10 to human-friendly Base 8.


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