If there is a prime number x, if we reciprocate it we will get 1/x.

Reciprocal of prime number will be a rational number , Except 1/2 and 1/5 , every number which is reciprocal of prime number is a recurring non terminating decimal number.

Question- How to find that after how many digit recurring numbers will repeat ? How to find the recurring numbers?


marked as duplicate by MJD, Chris Janjigian, Namaste, colormegone, ml0105 Apr 30 '14 at 17:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Except 1/2 and 1/5 $\endgroup$ – user136567 Apr 30 '14 at 16:23
  • $\begingroup$ @MJD In above question link conditions are given . How to calculate without any condition ? Here in my question numerator is 1. So its different. $\endgroup$ – user136567 Apr 30 '14 at 16:29
  • $\begingroup$ The period $n$ in which $\frac1p$ repeats is the smallest $n$ such that $10^n-1$ is a multiple of $p$. For example, $10^6-1 = 999999$ is a multiple of $7$, but $10^5-1$ is not, so $\frac17$ repeats every 6 digits. However, no general rule is known that describes the smallest such $n$ in general. $\endgroup$ – MJD Apr 30 '14 at 16:29
  • $\begingroup$ (The question has come up here many times before; a search for “period of decimal” will produce many relevant answers.) $\endgroup$ – MJD Apr 30 '14 at 16:30
  • $\begingroup$ For example, there are three answers at Compute the period of a decimal number a priori $\endgroup$ – MJD Apr 30 '14 at 16:33