the art of computing by decimal fractions. See Arithmetic.

Circulating Decimals, called also recurring or repeating decimals, are those in which a figure or several figures are continually repeated. They are distinguished into single and multiple, and these again into pure and mixed.

A pure single circulate is that in which one figure only is repeated; as .222, &c. and is marked thus .2.

A pure multiple circulate is that in which several figures are continually repeated; as .232323, &c. marked .23; and .524524, &c. marked .524.

A mixed single circulate is that which consists of a terminate part and a single repeating figure; as 4.222, &c. or 4.2.

And

A mixed multiple circulate is that which contains a terminate part with several repeating figures; as 45.524.

That part of the circulate which repeats is called the repetend; and the whole repetend, supposed to be infinitely continued, is equal to a vulgar fraction whose numerator Dr Wallis, it appears, was the first who distinctly considered or treated of infinite circulating decimals, as he himself informs us in his Treatise of Infinites.