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Decimal Representation of Rational Numbers
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A rational number is a number that can be written in the form p/q where p and q are integers, and q ≠ 0. The set of rational numbers is denoted by Q or
Q
. Examples:1/4, −2/5, 0.3 (or) 3/10, −0.7(or) −7/10, 0.151515... (or) 15/99. Rational numbers can be represented as decimals. The different types of rational numbers are Integers like -1, 0, 5, etc., fractions like 2/5, 1/3, etc., terminating decimals like 0.12, 0.625, 1.325, etc., and non-terminating decimals with repeating patterns (after the decimal point) such as 0.666..., 1.151515..., etc.
Decimal Representation of Rational Numbers
The decimal representation of a rational number is converting a rational number into a decimal number that has the same mathematical value as the rational number. A rational number can be represented as a decimal number with the help of the long division method. We divide the given rational number in the long division form and the quotient which we get is the decimal representation of the rational number. A rational number can have two types of decimal representations (expansions):
Terminating
Non-terminating but repeating
Note: Any decimal representation that is non-terminating and non-recurring, will be an irrational number.
Let's try to understand what are terminating and non-terminating terms. While dividing a number by the long division method, if we get zero