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How did decimal fractions become part of arithmetic in the Islamic world?

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arithmetic A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”

In the Islamic world, the development of decimal fractions emerged from a tradition of arithmetic books that began in the 9th century, largely inspired by the work of Muḥammad ibn Mūsā al-Khwārizmī. His influential book on Hindu calculation introduced the Indian decimal system for whole numbers to Islamic scholars.12

By the 10th century, mathematicians such as al-Uqlīdisī and al-Baghdādī extended this system to include decimal fractions, initially utilizing them as computational devices. These fractions were further refined in subsequent centuries, receiving systematic treatment as a general method for approximating irrational quantities.23

This evolution was supported by the interaction between arithmetic and algebra, as scholars drew analogies between working with powers of 10 and powers of an unknown variable. By the 15th century, mathematicians like Jamshīd al-Kāshī were using decimal fractions with great sophistication, including a highly accurate computation of $2 π$ .23