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INTRODUCTION OF RATIONAL NUMBERS

__RATIONAL NUMBERS -__

**Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number is any number that can be written in the form ๐/๐โ, where ๐ and ๐ are integers and ๐ โ 0.**

__Here are some key properties of rational numbers:-__

__Closure under Operations:-__The sum, difference, product, and quotient (except division by zero) of any two rational numbers is also a rational number.__Repeating or Terminating Decimals:-__Every rational number can be represented as either a terminating decimal (e.g., 3/4 = 0.75) or a repeating decimal (e.g., 1/3 = 0.3โพ ).__Equivalent Fractions:-__Rational numbers can have an infinite number of equivalent fractions. For example, 1/2 = 2/4 = 3/6 =โฆ.................__Ordering:-__Rational numbers can be ordered on the number line. For any two rational numbers ๐/๐โ and ๐/๐ โ, if ๐/๐ < ๐/๐ โ, then ๐๐ < ๐๐.

**Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number is any number that can be written in the form ๐๐qpโ, where ๐p and ๐q are integers and ๐q is not equal to zero.**

**Rational numbers include integers, fractions, and terminating or repeating decimals. Here are some examples of rational numbers:**

**Integers: โ3, 0, 1, 7**

** 1 3 5**

** 2. Fractions: ------, ------, โ ------**

** 2 4 6**

** 1 3 7**

** 3. Terminating decimals: 0.25 = -----, 0.6 = -----, โ1.75 = โ -----**

** 4 5 4**

** 1 2 1**

** 4. Repeating decimals: 0.3โพ= -----, 0.6โพ= ------, 0.142857โพ= -----**

** 3 3 7**

**It's important to note that every integer is also a rational number, as it can be expressed as a fraction with a denominator of 1 (e.g., 5 = 5โ/1). Additionally, irrational numbers, such as โ2โ or ฯ, cannot be expressed as fractions of integers and are not considered rational numbers.**

**Rational numbers are closed under addition, subtraction, multiplication, and division, meaning that the result of any arithmetic operation on rational numbers is also a rational number. They form an important part of the number system and are used extensively in mathematics, science, and everyday life.**

**ยช IMPORTANT TO KNOW:-**

**1. Every integer
(positive, negative or zero) is a rational
number.**

**2. Every fraction
is a rational number.**

**The rational
number(-p/q) can be written as โ (p/q).**

** p/q is a positive
rational number and -p/q is a negative
number.**