# MSC #29: Using the Ekadhika

Can you solve this problem in less than 3 seconds?

“What are the last four digits in the recurring pattern in the decimal equivalent of 1/19?

A) 6667; B) 0526; C) 8421; D) 9991; E) 3829”

This problem, which was given in the intermediate level of the 1st International Vedic Mathematics Olympiad cannot be solved using an ordinary calculator because the recurring decimal string is 18 digits long. Manually dividing 1 by 19 will take too much time and very few will actually attempt it.

But by using the Ekadhika, which is the topic of the 29th of our 30 MATH-Inic Specials for Christmas series, we can know the answer in less than 3 seconds.

Our 29th MATH-Inic Special for Christmas is about a “fun, fast and easy” way to convert a fraction with a prime number denominator into a recurring decimal. In our example here, instead of dividing by 19, we will use its Ekadhika, 2 . The Ekadhika is also discussed in Chapters 1 and 15 of the “30 Master Strategies in Computing”