138                     Numeration.

PART III."

DECIMAL FRACTIONS.

NUMERATION.

In Decimal Fractions the integer, or whole thing, as one pound, one yard, one gallon, &c. is supposed to be divided into ten equal parts, and those parts into tenths, and so on without end.

So that the denominator of a decimal, being always known to consist of a unit, with as many cyphers as the numerator has places, is therefore never set down; the parts being only distinguished from the whole numbers by a comma prefixed ; thus, ,5 which stands for -^;  ,25 -^ ;  ,123 for f^.

But the different value of figures appears plainer by the following table.

Whole numbers. Dechnal parts. 7654321234567

i  ^1  r—1  U    i-(    U    — ¦  1*

From which it plainly appears, that as whole numbers increase in a tenfold proportion to the left-hand, decimal parts decrease in a tenfold proportion to the right-hand ; so that cyphers placed before decimal parts decrease their value by removing them farther from the comma, or unit's place ; thus, ,5 is 5 parts of 10 or -j^; ,05 is 5 parts of 100, or r&T3 > |OOS is 5 parts of 1000, or -roW > ,0005 is 5 pmts of 10000, or -1-5-5-5-5. But cyphers after decimal parts do nut siter (heir value, for ,5 ,50 ,500 &c. are each but -^ of the unit.