i8 ELEMENTS OF SCIENCE 



how many units of that " denomination " the fraction in 

 question consists. 



Here the root number 10 comes again into play in a 

 way analogous to that before mentioned. 



A tenth part being written -f^ , the tenth part of a 

 tenth part, is expressed by adding a zero to the right, 

 yj-g-, and so on indefinitely. 



This fact has suggested a further development of the 

 system previously described. 



"We saw that in any series of figures expressing a 

 number, the figure at its right extremity signifies units, 

 while each succeeding figure to the left expresses a 

 higher power of ten. Now evidently we may also add 

 figures to the right of the figure expressing units, and 

 then each succeeding figure will express a decreasing 

 power of ten, just as well as a fraction will, and we 

 place a point to indicate the spot where this decrease 

 begins. Thus one and one-tenth, which we may write 

 as ij 1 ^, may be equally expressed by i.i, and similarly : 



o~o by i.ooi, and so on. 



Thus 892.35 means, 8 groups of ten times ten units, 

 9 groups of ten units, 2 units, 3 groups of tenths 

 of units, and 5 groups of hundredths of units. 



So far we have dealt only with enumeration according 

 to the radix 10 the decimal system of notation. But, as 

 before said, the employment of this radix simply arose 

 from the number of our fingers and toes. "We may take 

 any number as a radix, but if we had had six digits on 

 each hand, the radix we should have taken would no 

 doubt have been 12, which would have constituted 

 a duodecimal system of notation. This would have 



