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# Class9 number system

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### Class9 number system

1. 1. Rational and Irrational number Rational numbers are in the form of p/q where p and q both are integers and q is not equal to 0 Eg 2/5 , 4/7 ,7/20
2. 2. Number System Irrational number Rational numbers Integers Whole numbers Natural numbers
3. 3.  Real numbers The collection of irrational and rational numbers are called as real numbers. Every real number can be represented by a unique point on a number line. Two German Mathematician Cantor and Dedekind showed that corresponding to every real number there is a point on the real number line.
4. 4. Terminating and non terminating decimals  The decimal expansion of a rational number is either terminating or non terminating recurring.  Irrational numbers are non terminating and non repeating.
5. 5. Examples of irrational numbers  √2 , √14  √24 , √10  √12, √7 All the numbers can be represented on a number line
6. 6.  If the denominator in the rational number in the lowest form is the multiple of 2 or 5 or both then the number is terminating  Eg 3/ 128 The denominator can be represented in the form of 27 ,hence the number is terminating.
7. 7. Rationalising the denominator  If we have a number 1/√7 We can rationalize the denominator by multiplying the number by √7 We get 1/√7 x √7/ √7 √7/ 7
8. 8.  Every point on a number line represents a real number.  We can represent √2 , √3, √5 on a number line
9. 9. Representation of irrational on number line
10. 10. Conclusion  Rational numbers are either terminating or non terminating repeating decimals  Irrational numbers are non terminating non repeating decimals.  Every real numbers can be represented on a number line  Every point on a number line represents a real numbers.