Analysis of Vedic Mathematics EKADHIKENA PURVENA Sutra in Decimal Representation of a Fraction

Abstract

Vedic Mathematics, an ancient Indian mathematical system derived from the Atharva Veda, is renowned for its simple, logical, and rapid computational methods. Among its sixteen principal sutras, “EKADHIKENA PURVENA”—which means “by one more than the previous one”—is particularly significant for determining the decimal representation of fractions whose denominators end with the digit 9. This sutra provides a precise method for obtaining recurring decimals without the use of long division. According to this principle, at each step, one adds one to the previous digit to generate the successive decimal numbers. For instance, fractions such as, or can be expanded quickly and accurately using this sutra.

The application of this principle not only enhances the speed and efficiency of mental calculations but also reveals the logical structure and profound mathematical insight embedded in the Vedic system. This study presents the theoretical foundation of the EKADHIKENA PURVENA sutra, explains its step-by-step application, and compares its effectiveness with conventional long division methods for deriving recurring decimal sequences.