# CHAPTERS BY WACEK KIJEWSKI

# # Chapter 02 The “Power of Ten” Notation

*Basic and applied sciences are interwoven, they are like a tree whose roots correspond to basic science. If the roots are cut, the tree will degenerate. Basic science fosters a kind of attitude that will be most productive in whatever work will finally end up with...Training in basic science often produces the best candidates for applied work.
Victor Weisskopf, the recipient of the International Commission on Physics Education award, speaking
at the AAAS in Boston, 1993*

Science deals with enormous ranges of quantities. Some of them are very small like the size of an atom or the mass of an electron, and some are very large like the distance between stars or the mass of a planet.

In order to represent such different ranges, the SI system of measurements utilizes an exponential presentation of number in the form of “power of ten”, sometimes called an “order of magnitude”.

For example we could express the distance to the nearest star Alpha Centauri as 40 400 000 000 000 000 meters or 4.04 × 10

^{16}meters. Obviously, the last expression is a simpler number to operate with.

The first step is learning the SI system of measurements, therefore, is to acquire mathematical skills in the manipulation of number expressed in the “power of ten” notation.

**THOSE DAMNED DOTS! GROWING PAINS OF ADAPTATION**

One of the meanest tricks that evolution could play on a species destined to do arithmetic is to give it hands with five fingers on them. Any self–respecting numerate organism would prefer four or, at a pinch, eight digits. This is because, as computer scientists were quick to work out, the most efficient way to count is in powers of two (i.e. 1, 2, 4, 8, 16…). Instead, humanity is stuck with the decimal system; its two five-appendaged hands have made it almost inevitable. Mankind, except for some nostalgic shilling–and–furlong Englishmen, counts in tens instead of twos...

However British shares and government bonds have been traded in multiples of a 32nd of a pound since time immemorial. The decimalization of the currency in 1971 made no difference to this tradition. Nor did the fact that Continental Europeans, influenced by the perfidious doctrine of metrication that the French revolution invented and Napoleon disseminated, long ago decided to quote their stock prices decimally... American securities of all sorts are also frequently quoted in powers of two (1/2, 1/4, 1/8…) Or, rather, were… for stock markets and banks in UK and USA are now abandoning the familiar fraction in favor of the dreaded decimal! O tempora! O mores! 0.03125!

© *The Economist, London, 7th June, 1997 (abridged)
Reproduced by permission*

#### DID YOU KNOW ????

All information about you is recorded in 6 000 000 000 genes contained in your body. Some genes are thought to be able to record your experience and pass in to the next general-eration. (Gene = a unit of heredity; from Greek genes = born).

Do you like anecdotes, interesting and challenging problems, fun facts, puzzles, jokes related to metric system and measurement? Read them in the 2006 on-line edition of "SI Units, Conversion and Measurement Skills",186 pp.