Coins of the Indian rupee 3, 5, 10, 20, 25, 50 (naya) paisa and one rupee. Since rupees retained their pre-decimal value, pre-decimal coins of one, half and quarter rupees remained in circulation after decimalisation. The word "naya" was dropped in 1964 and a new denomination, the 3 paisa, was introduced into circulation. A 20 paisa coin was minted in 1968. Neither of these coins gained much popularity. The 1, 2 and 3 paisa coins were phased out gradually in the 1970s. In 1982, a new 2 rupee coin was introduced experimentally to replace 2 rupee notes. The 2 rupee coin was not minted again
Decimal decimal fractions were non-positional. However, counting rod fractions were positional. Qin Jiushao in his book Mathematical Treatise in Nine Sections (1247) denoted 0.96644 by J. Lennart Berggren notes that positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century. The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350, anticipating Simon Stevin, but did not develop any notation to represent them. The Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century. Al Khwarizmi introduced fraction to Islamic countries in the early 9th