XVI COMPUTATION KILES. 



Separate the number into two factors, the first being the original 

 number with the decimal point changed in position so as to follow the 

 first figure; the other being lo 1 ", where the sign is plus for a whole 

 number and minus for a fraction, and where n is the number of places 

 the decimal point has been moved. 



To transform a number expressed in this way bark into the onli- 



!<rm. move the decimal point n places, making the number a 



whole (or a larger) number if n is plus, and a fraction if n is minus. 



Associate firmly in the mind the plus sign with whole numbers, 

 the minus sign with fractions ; thus avoiding confusion as to the 

 si,u r n of ?i. 



In much work, the factoring need not be written out, but may 

 merely be mental. 



This notation reduces the error and work of locating the decimal point in 

 multiplication or division, especially in expressions containing several terms 

 in the numerator and denominator. It is very helpful in connection with the 

 characteristic of logarithms, and the location of the decimal point in evolution, 

 involution, and finding reciprocals. It saves space and promotes clearness in 

 expressing large numbers or small fractions, and it is the best aid in following 

 the decimal point while using the slide rule. It also enables one to dispense 

 with characteristics in certain parts of computations (see Examples, page xxi). 



An abbreviated notation helpful in one's own work, but perhaps not to be 

 urged for general adoption, consists in dropping the -10, thus, 



instead of ^oy'io 2 write merely 4.5072 

 instead of 5.3704 - io~ 3 write merely 5. 3704-3 



The adoption of the bracket or parenthesis, e.g. (4.507)2, for either notation 

 in cases of possible doubt removes all risk of mistaking these indices for ordinary 

 exponents of powers. 



Examples 9, 10, n give incidentally illustrations of the use of the notation 

 by powers of 10. 



Symmetrical Grouping of Figures. For writing numbers, adopt 

 the following system of groups and spaces : 



Write 143 258.64 796 



instead of 143,258.647,96, the usual method. 



A still clearer method would be to write 

 143 25864 796 



It-noting the units' place by the heavy figure, but this is impracti- 

 cable. The proposed system is symmetrical about the units' place, 

 the customary system, is not. It groups together the units, tens, 

 and hundreds of thousandths, of millionths, etc., as well as of thou- 



