Trace the diffusion of zero and decimal numerals from India to the Arab world and to Europe.

• A. Origin in China; transmitted to Europe via merchants.
• B. Origin in Greece; transmitted to Arab world via translations.
• C. Origin in Arabia; spread to India and Europe.
• D. Origin in India; transmitted to the Arab world by scholars; later transmitted to Europe via translations; widely adopted.

Answer: (D)

Zero and decimal numerals originated in India as part of the Hindu-Arabic numeral system, with zero developed as a number and as a place-holder and decimal place-value notation established by Indian mathematicians. From India these ideas spread to the Arab world through scholars who translated and studied Indian mathematical treatises in centers like Baghdad during the Islamic Golden Age, where the numerals were adopted and used in arithmetic and astronomy. The system then traveled from the Arab world to Europe via Latin translations of Arabic texts in places such as Toledo and Sicily, aided by traders and scholars who carried new methods of calculation back to medieval Europe. In Europe, the Hindu-Arabic numerals, once translated and taught, gradually replaced Roman numerals and became widely adopted by the late Middle Ages and Renaissance, aided by works such as Fibonacci’s Liber Abaci that popularized the new notation.

The other options misplace where the numerals originated or how the diffusion occurred: they either attribute the origin to China, Greece, or Arabia, or they omit the crucial step of India as the source and the role of translations into Latin before Europe adopted the system.