C 211 ] 
For + 
IO 1 
T 
IOO 
+ 
— 4- — . 4 . 
OO I 1*0000 I 
IOO 
I 
IOOO 
+■ 
ioooooo 
But 1 1 1 &c. x 9 
ioi o i &c. x 99 
loo i oo i &e. x 99^9 
I 
+ 
&c. 
100 — 10 -f- t 
T~ ill ©it. 
1000 
IOOO 
IOOO ©C* 
I 
+ 
&C: 
ioooo 100 -j- t 
IOIOI © 6 . 
- IOOOOOO 
IOOOOOO 
IOOOOOO ©c. 
I 
-1- 
&C, 
___ ioooooo ~f- 1000 t 
IOOIOOI 
IOOOOOOOOO 
IOOOOOOOOO 
IOOOOOOOOO ©c . 
1000 
&c. (by 3 d ) Then - 
I T I ©C . „ I 
1000 ©c. 9 
iooooo &c. 
iooooooooo &V. 
Then 
Then 
IOIOI &C. , I 
IOOOOOO e?C. 
IOOIOOI &V. 
iooooooooo ©’c. 
I 
99 
i 
999 
Hence the reciprocal of a number confifting of n places of 9’s, is 
equal to a circulating number of n places, the right hand figure being 1, 
and the reft o*s. 
Thus, l — 
9 
1 . 
99 
1 
999 
1 
, 9999 
III &c. 
1000 &c . 
10101 ©V. 
IOOOOOO ©V. 
1001001 &ff. 
iooooooooo. & c. 
= 0,1 
• 1 
= 0,01 
. 1 
== 0,001 
IOOOIOOI, 
iooooooooo o®d ©c. 
= 0,0001 . 
6. If the reciprocal of a number confifting of n places of 9 s > b e multi- 
plied by. a number D, not exceeding n places j the product will be a cir- 
culating decimal fraction of n places, the right hand ones being the fame 
digits as are in the number D. 
Let D = 3 j or D = 23 j or D = 785 ; orjo any other number* 
Eea 
Now 
