DoorstepTutor (NEET, JEE, IMO, NSO, NTSE...)'s video: Rational Number : Terminating and Recurring Condition for Denominator Making a Terminating Decimal

Rational numbers are of the form p/q where p and q are integers and q is not zero. Rational numbers when converted to decimal can be terminating or non-terminating. Rational Numbers: Terminating * Let 𝑥 be a rational number whose decimal expansion terminates. Then we can express 𝑥 in the form 𝑥 = 𝑝/𝑞, where p and q are coprime, and the prime factorization of q is of the form 2^𝑛 5^𝑚, where 𝑛, 𝑚 are non-negative integers * Let 𝑥 = 𝑝/𝑞 be a rational number, such that the prime factorisation of 𝑞 is of the form 2^𝑛 5^𝑚, where 𝑛, 𝑚 are non-negative integers. Then 𝑥 has a decimal expansion which terminates. Rational Numbers: Recurring Let 𝑥 = 𝑝/𝑞 be a rational number, such that the prime factorisation of q is not of the form 2^𝑛 5^𝑚 , where 𝑛, 𝑚 are non-negative integers. Then 𝑥 has a decimal expansion which is non-terminating repeating (recurring).