Explanation 
of the abbreviated Tables from 10000 to 1,111,111. 
The preceding Tables are designed for Mul 
tiplications and Divisions of concrete numbers to 
the extent of, for instance, 99 Doll. 99 Cents 
For the calculation of greater, numerical values 
the following Tables, from 10000 to 1,111,111 
(and even higher if required) are intended, and to 
be used conjunctly with the preceding Tables. 
The author being aware that by continuing 
the arrangement of the Tables beginning with 
10000 in the same manner as those from 1 to 
9999, the book would be swelled up to a volume 
of some 5500 pages and thus lose in its purport 
to be a cheap and handy means to aid accountants 
in their arduous task: he compiled these present 
Tables in a manner which, though essentially 
abridged, will nevertheless not in the least di 
minish the utility of them. 
This shortening is effected by printing all the 
Products, on the right and left of the middle cMumn, 
not in their complete form, but by producing only 
the Ten - thousands and upwards (Ten-thousands, 
Hundred-thousands, Millions) whilst the Units, Tens, 
Hundreds, and Thousands are always omitted. 
Suppose that 1,111,111 was to be multiplied 
by 9, the example would appear thus; 
1111111 
9 
9999999 
The first three (big) figures of the Product 
will be found in the present abbreviated Tables, 
the other four, however, must be looked for in the 
preceding (complete) Tables from 1 to 9999. 
From this it appears that in multiplying any 
number above 10000 by any other number, the 
Products of Ten-thousands and upwards will be 
found in the abbreviated Tables — whilst the 
complete Tables, up to 9999, must be referred to 
for the Products of the Units, Tens, Hundreds, 
and Thousands (the f o u r last figures of the Mul 
tiplicand). Should it happen that in a Multiplicand 
exceeding 10000, that portion of it which is to be 
looked for in the complete Tables, is only a unit, 
the wanting Tens, Hundreds, and Thousands must 
be filled up with ciphers. For instance: 
First illustration. To multiply 10002 by 
9, the Multiplicand is divided into 10000 and 2. 
The first number we find in the middle column 
of the abbreviated Tables (1st Table) . 10000 
the other in the complete Tables (Table 1) . 2 
' 10002 
The Products will be found in the column 
under 9 
in the abbreviated Tables: = 9 
„ „ complete „ =18 
Two ciphers must be put before the 
Product 18 to render it one of four 
figures 00 
and the problem is solved: 10002 X 9 = 90018 
In multiplying the same number by 90, 900, 
9000, etc. as many ciphers as are contained in the 
Multiplicator must be added to the above obtained 
Product. 
Second illustration. 
410999 X 9. 
To effect this we look in the 
middle column of the abbreviated 
Table for 410000 X 9 = 369 
of the complete Table 999 X 9 — 8991 
and obtain 410999 X 9 = 3698991 
Third illustration. 499999 X 9. 
In the abbreviated Tables: 498889* X 9 = 449 
„ complete „ 9999 X 9 — 9991 
499999 X 9 = 4499991 
*) The reckoner must always bear in mind that, in 
order to get at the correct Product, he must look in the 
middle column of the abbreviated Tables always for the 
number next in size, but smaller, to that of the Multipli 
cand. In this case it is therefore not the number 490000, 
as might erroneously be believed, but the number 498889, 
as being next in size to the Multiplicand 499999. 
From this rule also follows that the Product taken 
from the complete Tables must be of four figures only; in 
this case, therefore: 9999 x 9 — 89991.