IlTTATIoN Kl'LES. XV 



tion under the foregoing rules for addition or subtraction 



Mial place each of these terms must be carried. 

 Further, n and /; must each be carried to the number of significant 



:ms required in the product //', and so on. 



In complicated formula- this process of inspection is sometimes 

 slightly troublesome, b ntial unless the necessary pr 



of the components has been otherwise studied: as, for example, by 

 :nple applications of the diiferential calculus as in the author's 

 >M of Measurements." 



,-ii. pa-<' \... 1'ractical examples of substitution in 

 moderately simple forum: 



NOTATION BY POWERS OF TEN. 



Statement of the Method. Regard the decimal point as merely 

 an allix whose sole purpose is to indicate which is the units' place 

 Fix the attention firmly upon the units' place as the centre 

 of symmetry of our customary system of notation. The too un; 



ice to the decimal point, rather than to the units' pi; 

 arithmetical rules and explanations, has remitted in masking this 

 symmetry and in thus depriving the student of its important aid. 

 :nm<>n decimal system of notation, a elicit in the units' 

 place : . many times unity. />. BO many times io( = l), 



or SO man;. In the tirst place to the left of the units' place 



- so many times 10 '. f.e. BO many /./, and in tin- 

 to the ri.^ht. so many ti: -> many f< >fJ>s ; in 



coiul place to the h-ft so many times i> ind t<> 



;iv t ini' it//* ; in the ^ixth pla 



- '' and io~' J . /.'-. titflliHiix and millionth*, resjicct ively : 

 OIL 'I'he fundamental symmetry of the whole system 

 .ml should not be l..st sight of. 



In counting up places, whether to right or left, always begin with 

 the units' place as zero. 



:. then, that we may write numbers in this way: 



case may teq 



'I'll. 



