How did Bhaskara II use the decimal number system systematically?

Bhāskara II, a prominent 12th-century mathematician, is recognized for authoring the first work that employed the decimal number system in a full and systematic manner.1

While the decimal place-value system had been in use among Indian mathematical professionals since at least the early 1st millennium CE, Bhāskara II integrated this system into his foundational texts, such as Līlāvatī and Bījagaṇita. In these works, he utilized the system to compile and solve complex mathematical problems, including indeterminate equations of the first and second degrees.21

His systematic application extended to advanced algebraic techniques, where he used letters to represent unknown quantities and anticipated modern conventions for signs. By building upon the work of his predecessor Brahmagupta, Bhāskara II refined the use of these numerals to solve sophisticated problems, such as the Pell equation, and to calculate precise approximations of π. His contributions were instrumental in advancing Indian mathematics by formalizing the utility of the decimal system in both theoretical and applied contexts.1