What is a Rational Number
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What Is A Rational Number
What Is A Rational Number
Any number which can be expressed in the form p/q, where p and q are positive or negative integers and p can be zero, bjut not q, is a rational number. As 10 = 10/1, where p = 10 and q = 1 are integers => 10 is a rational number. Thus, all integers, fractions, recurring decimals, are rational numbers. A number of the type √2 is an irrational number as it can be proved that √2 cannot be expressed in the p/q form. Also, irrational numbers will be such fractions that they cannot be expressed as decimal or recurring decimal number. If one tries to express √2 in the decimal form, it is a never ending decimal number and there is no recurring pattern too.a rational number can be expressed as a ratio (a/b) where a and b are integers and b not equal to 0. the decimal number of rational number is either terminating or repeating decimal.
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examples: 1/6, 3.343434 irrational number : any real number which cannot be expressed as a ratio (a/b) where a and b are integers and b not equal to 0 and is therefore irrational number is not a rational number. the decimal number form an irrational number is neither terminating nor repeating decimal. 1. Closure property of rational numbers: Closure property holds true for all mathematical operators, which means that if p1/q1 , p2/ q2 are any two rational numbers then a) b) c) d) their sum ( p1/q1) + ( p2/ q2) is a rational number their difference ( p1/q1) - ( p2/ q2) is a rational number their product ( p1/q1) * ( p2/ q2) is a rational number their quotient ( p1/q1) ÷ ( p2/ q2) is a rational number
2. Power of Zero: In the set of rational numbers, there exists a number zero such that if the number zero is added to an number, it does not change the value of the rational number, i.e. p1/q1 + 0 = p1/q1. On another hand if this rational number zero is multiplied to any of the rational number, then it results to zero ,i.e. ( p1/q1) * 0 = 0 Eg : ( 3/5 ) + 0 = ( 3/ 5) And ( 3/5 ) * 0 = 0
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3. Multiplication by 1: 1 is called the Multiplicative identity of the rational numbers, which means that if any rational number p1/q1 is multiplied to 1, the result is unchanged, i.e. p1/q1 * 1 = p1/q1. For example: ( 3/5 ) * 1 = 3/5 4. Rational numbers are dense: It indicates that there exist infinite and uncountable sets of rational numbers. This also means that the number of rational numbers is endless. Between any given two rational numbers, there exist again uncountable rational numbers So the set of rational numbers is called a dense set. We must remember the following facts about rational numbers: A) All negative rational Numbers are always less than 0. B) All positive rational Numbers are always greater than 0. C) All negative rational Numbers are always less than any positive rational numbers. D)In order to compare two rational numbers, which are if both negative or both positive rational numbers, we need to make the denominators same and then compare them.
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What Is A Rational Number
Any number which can be expressed in the form p/q, where p and q are positive or negative integers and p can be zero, bjut not q, is a rational number. As 10 = 10/1, where p = 10 and q = 1 are integers => 10 is a rational number. Thus, all integers, fractions, recurring decimals, are rational numbers. A number of the type √2 is an irrational number as it can be proved that √2 cannot be expressed in the p/q form. Also, irrational numbers will be such fractions that they cannot be expressed as decimal or recurring decimal number. If one tries to express √2 in the decimal form, it is a never ending decimal number and there is no recurring pattern too.a rational number can be expressed as a ratio (a/b) where a and b are integers and b not equal to 0. the decimal number of rational number is either terminating or repeating decimal.
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examples: 1/6, 3.343434 irrational number : any real number which cannot be expressed as a ratio (a/b) where a and b are integers and b not equal to 0 and is therefore irrational number is not a rational number. the decimal number form an irrational number is neither terminating nor repeating decimal. 1. Closure property of rational numbers: Closure property holds true for all mathematical operators, which means that if p1/q1 , p2/ q2 are any two rational numbers then a) b) c) d) their sum ( p1/q1) + ( p2/ q2) is a rational number their difference ( p1/q1) - ( p2/ q2) is a rational number their product ( p1/q1) * ( p2/ q2) is a rational number their quotient ( p1/q1) ÷ ( p2/ q2) is a rational number
2. Power of Zero: In the set of rational numbers, there exists a number zero such that if the number zero is added to an number, it does not change the value of the rational number, i.e. p1/q1 + 0 = p1/q1. On another hand if this rational number zero is multiplied to any of the rational number, then it results to zero ,i.e. ( p1/q1) * 0 = 0 Eg : ( 3/5 ) + 0 = ( 3/ 5) And ( 3/5 ) * 0 = 0
Read More About Irrational Numbers Worksheet
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3. Multiplication by 1: 1 is called the Multiplicative identity of the rational numbers, which means that if any rational number p1/q1 is multiplied to 1, the result is unchanged, i.e. p1/q1 * 1 = p1/q1. For example: ( 3/5 ) * 1 = 3/5 4. Rational numbers are dense: It indicates that there exist infinite and uncountable sets of rational numbers. This also means that the number of rational numbers is endless. Between any given two rational numbers, there exist again uncountable rational numbers So the set of rational numbers is called a dense set. We must remember the following facts about rational numbers: A) All negative rational Numbers are always less than 0. B) All positive rational Numbers are always greater than 0. C) All negative rational Numbers are always less than any positive rational numbers. D)In order to compare two rational numbers, which are if both negative or both positive rational numbers, we need to make the denominators same and then compare them.
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