The Index Notation

THE INDEX NOTATION Origin.—The need which modern science has created for decimal fractions to a large number of decimal places has led to the introduction of a new symbolism based upon the fact that A-„= i o-", and hence that 10 0 0 0 -- = i shorter way of expressing the common fraction. For example, instead of saying that a millimicron is 0•00000000i of a meter, we may say that it is ; and instead of saying that a square millimeter is 0.00155 of i sq. in., we may say that it is sq. in. or 155Xio 5 sq. in. The index notation is also used in connection with very large numbers, as when we express 750,000,000,000,000 ultra violet waves per second as per second.

Advantages of the Index Notation.

The demands of astronomy and physics render it necessary to use numbers to represent such great and such small distances and lengths that the eye has difficulty in detecting their meaning when they are written. The index notation not only condenses the statement but it is particularly valuable when logarithms are to be used.

For example, in the case of 1.55X we see that the character istic of the logarithm is and in the case of 7.5XIO14 it is 14 Since a fraction expressed in any one notation can be expressed in any other, it is immaterial what notation is used so far as the general principles of fractions are concerned.

BIBLIOGRAPIIY.-On

the general theory of fractions consult E. ComBibliograpiiy.-On the general theory of fractions consult E. Com- bette, Cours d'Arithmetfque (12th ed., 1994) ; A. Hofler, Didaktik des mathematischen Unterrichts (Leipzig, i91o). (Foundation principles.) On the history of the subject consult J. Tropfke, Geschichte der Ele mentar-Mathematik. 2nd ed., 1921, Berlin (de Gruyter), vol. i., p. 118-49; D. E. Smith, History of Mathematics (Boston, 1925), vol. ii., PP. 208-27, 418-20, 477-93. (General development of the various types of fraction, with facsimiles from early works.) (D. E. S.)