Class9 number system
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Rational numbers are numbers that can be represented as fractions p/q where p and q are integers and q is not equal to 0, such as 2/5 or 4/7. Irrational numbers are numbers that cannot be represented as fractions, such as √2 or √3, and their decimal representations are non-terminating and non-repeating. Real numbers include both rational and irrational numbers and can all be represented as unique points on a number line, with rational numbers having either terminating or non-terminating repeating decimals and irrational numbers having non-terminating, non-repeating decimals.
Class9 number system
- 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
- 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. 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. Examples of irrational numbers √2 , √14 √24 , √10 √12, √7 All the numbers can be represented on a number line
- 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. 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. Every point on a number line represents a real number. We can represent √2 , √3, √5 on a number line
- 9. Representation of irrational on number line
- 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.