C * 5 * * * * 10 ] 
The circulating fraction 0,999, & c - equal to ! >o. 
For the difference between 1,0 and 0,999 * s lefs than can be 
aftigned. 
To fave a repetition of figures, it is ufual to mark the firfl and lafl of 
circulating expreffions, with points over the figures. 
Thus, 0,333 &c. is wrote 0,3 ' 
• • •• 
0,2323 &c. 0,23 • 
0,785785 &c. 0,785 
- - «• 
4. Like circulating decimal fractions are thofe which have each the fame 
number of circulating places ; and begin to recur each at the fame name. 
Every finite decimal fradion may be confidered as infinite ; cyphers being 
ufed as the circulating part. 
Either place of a circulating expreflion may be taken as the firfl ; obferv- 
ing that the number and order of the circulating places be not altered. 
For as the decimal fradion arifes by divifion ; if either place of the re- 
curring figures be taken for the firfl, the others will from thence re- 
gularly circulate. 
Hence feveral unlike circulating decimal fradions may be made to begin 
and end at places of like names. 
5. If in the decimal fcale to, 100, 1000, 10000, 100000, 1000000, &c. 
continued indefinitely, be feleded any rank of equi-difiant terms, fuch, 
that whatever term therein is taken for the firfl term, and the firfl term is 
made the common ratio to the reft ; then will the fum of the reciprocals of 
thofe terms, be equal to the reciprocal of the number which is unity lefs 
than the firfl term. 
Thus 
1 
T~o*o 
x 
TTot 
+ 
+ 
1 
*1 o 6 
1 
T"o o 'o’ 
1 
+ Wo-* -L; 10 being the i ft term. 
+ twUk +&c.=^ r ; .100 being the 1 (t term. 
+ rnWmiT + i ‘ 000 b ?> n g lhe 1 term ' 
' - I * 
For 
