14 ELEMENTS OF SCIENCE 



extreme right, but reserve the single group of 10 (out of 

 the 15) till we see how many groups of 10 will be 

 produced by the next step of multiplication. Our table 

 tells us again that 5 times 6 are 30, and the 6 there 

 multiplied (since it stands in the second place from the 

 right) denotes 6 groups of 10, so that 30 resulting from 

 its multiplication by 5 means 30 groups of ten, to which 

 we add the one group of ten reserved out of the 15 units 

 making 31. Of this 31 we again write down i, 

 reserving the 3 to be added to the sum of next 

 higher value. But the figure which stands next is a 

 cypher or zero, and 5 times nothing is, of course, nothing, 

 so all we have next to set down is the 3 we previously 

 held in reserve. Lastly comes the fourth figure 2 

 (denoting two groups, each of ten times ten times ten), 

 and this, when multiplied by 5, becomes 10, and so we 

 arrive at the result, " ten thousand three hundred and 

 fifteen," which sum we also obtained by simple addition. 

 Then comes the addition of 2063 to itself 40 times, which 

 is effected by multiplying the 2063 by a 4 which stands 

 in the second place, and therefore denotes not four units 

 but 4 groups of ten. We thus learn by a brief process 

 that 2063 added to itself forty times over conies to 

 82,520. The zero is not indeed written down in the 

 process because we have now nothing to do with mere 

 units, the 4 used in multiplying denoting, as before said, 

 only groups of ten. 



Similarly we can quickly see the result of adding 2063 

 to itself 300 times by multiplying the former sum by a 

 figure 3 standing in the third place, which is that set 

 apart for denoting what the number of hundreds may be. 

 We thus see that the addition of this sum to itself 300 

 times, amounts to the number 618,900. The two cyphers 

 are not written down because the multiplying figure 



