J. Lennart Berggren notes that positional decimal fractions were used for the first time by Arab mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century.[6] The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them.[7] The Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century.[6] Al Khwarizmi introduced fractions to Islamic countries in the early 9th century; his fraction presentation was an exact copy of traditional Chinese mathematical fractions from Sunzi Suanjing.[8] This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by 10th century Abu'l-Hasan al-Uqlidisi and 15th century Jamshīd al-Kāshī's work "Arithmetic Key".[8][9]