Decimal Representation of Rational numbers - Class 9 - R D Sharma and R S Aggarwal
Channel: Math Solutions Foundation
Date: 2021-03-08

In this video, you will get full explanation of decimal representation of rational numbers. This topic is given on page 1.6 of R D Sharma class 9th and on page 11 of R S Aggarwal Book of mathematics class 9th. This topic is very crucial to understand rational numbers.

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Every rational number p/q can be expressed as a decimal. On dividing p by q, two possibilities arise
     (i) The remainder becomes zero and the division concludes after a finite number of steps. In this case, the decimal expansion obtained also terminates or ends.
    (ii) The remainder never becomes zero and a repeating string of remainders is obtained. In this case, we get a digit or a block of digits repeating in the decimal expansion.
Thus, we have two types of decimal expressions:
1. Terminating Decimal : A decimal that ends after a finite number of digits is called a terminating decimal.
Important Rule : A rational number p/q is expressible as a terminating decimal only when prime factors of q are 2 and 5 only.
2. Repeating (or recurring decimals) A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring, decimal.
Special Characteristics of Rational numbers
(i) Every rational number is expressible either as a terminating decimal or as a nonterminating recurring decimal.
(ii) A number whose decimal expansion is terminating or nonterminating recurring is rational.