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MB0901 QR

  1. 1. In this document you can review important • Definitions • Facts • Formulae • Procedures Class – IX, CBSE MB0901: The Number System Learn Math for Free. Visit www.ganitgurooz.com
  2. 2. What is a Rational Number? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  3. 3. What is a Rational Number? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Rational Numbers A number is called a rational number, if it can be written in the form , where and are integres and 0. r p q p q q Learn Math for Free. Visit www.ganitgurooz.com
  4. 4. What is an Irrational Number? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  5. 5. What is an Irrational Number? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Irrational Numbers A number is called a irrational number, if it cannot be written in the form , where and are integres and 0. s p q p q q Learn Math for Free. Visit www.ganitgurooz.com
  6. 6. What is the nth root of a number x? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  7. 7. What is the nth root of a number x? Class – IX,CBSE MB0901: The Number System Important Definitions Topic: Rational Numbers The root of a number , is a number , if . th n n x y y x Learn Math for Free. Visit www.ganitgurooz.com
  8. 8. Fact # 1 The decimal expansion of a rational number is either terminating or non-terminating recurring. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  9. 9. Fact # 2 A number whose decimal expansion is either terminating or non-terminating recurring is a rational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  10. 10. Fact # 3 The decimal expansion of an irrational number is non-terminating non-recurring. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  11. 11. Fact # 4 A number whose decimal expansion is non-terminating non-recurring is an irrational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  12. 12. Fact # 5 All the rational numbers and irrational numbers taken together makes up the collection of real numbers. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Real Numbers Learn Math for Free. Visit www.ganitgurooz.com
  13. 13. Fact # 6 Every point on the number line represents one and only one real number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Real Numbers Learn Math for Free. Visit www.ganitgurooz.com
  14. 14. Fact # 7 Every real number has a unique location on the real line. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Real Numbers Learn Math for Free. Visit www.ganitgurooz.com
  15. 15. Fact # 8 The sum of a non-zero rational number and an irrational number is an irrational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  16. 16. Fact # 9 The difference of a non-zero rational number and an irrational number is an irrational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  17. 17. Fact # 10 The product of a non-zero rational number and an irrational number is an irrational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  18. 18. Fact # 11 The ratio of a non-zero rational number and an irrational number is an irrational number. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  19. 19. Fact # 12 The Pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Class – IX,CBSE MB0901: The Number System Important Facts Topic: Pythagoras’ Theorem Learn Math for Free. Visit www.ganitgurooz.com
  20. 20. Class – IX,CBSE MB0901: The Number System Important Formulae Topic: Rational Numbers For positive real numbers and , the following identities hold:a b 2 2 i ii iii iv v 2 a a ab a b b b a b a b a b a b a b a b a b a ab b Learn Math for Free. Visit www.ganitgurooz.com
  21. 21. Class – IX,CBSE MB0901: The Number System Important Formulae Topic: Rational Numbers Let 0 be a real number and and be rational numbers. Thena p q i ii iii iv qp q p q p pq p pp q p p q a a a a a a a a b ab a Learn Math for Free. Visit www.ganitgurooz.com
  22. 22. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n
  23. 23. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n : Locate the point on the number line.Call it A.nStep1
  24. 24. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n : Locate the point on the number line.Call it A.nStep1 : Drawa perpendicularABof length1unitatthepoint A.Step2
  25. 25. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n : Locate the point on the number line.Call it A.nStep1 : Drawa perpendicularABof length1unitatthepoint A.Step2 :Jointheorigin 0 tothepointB.Thislengthisequalto .nStep3
  26. 26. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n : Locate the point on the number line.Call it A.nStep1 : Drawa perpendicularABof length1unitatthepoint A.Step2 :Jointheorigin 0 tothepointB.Thislengthisequalto .nStep3 :Withcenteratorigin,andradiusOB,drawanarcintersectingthereallineatP.Step4
  27. 27. How to Locate an irrational number on the number line? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com n : Locate the point on the number line.Call it A.nStep1 : Drawa perpendicularABof length1unitatthepoint A.Step2 :Jointheorigin 0 tothepointB.Thislengthisequalto .nStep3 :Withcenteratorigin,andradiusOB,drawanarcintersectingthereallineatP.Step4 :The point P denotes on the number line.Step5
  28. 28. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  29. 29. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline.Step1
  30. 30. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts.p p Step1 Step2
  31. 31. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts. :Countaanda+1partsstartingfromp.Thesearepoints and 1 p p p a p a Step1 Step2 Step3
  32. 32. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts. :Countaanda+1partsstartingfromp.Thesearepoints and 1 :Magnifythelength , 1 p p p a p a p a p a Step1 Step2 Step3 Step4
  33. 33. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts. :Countaanda+1partsstartingfromp.Thesearepoints and 1 :Magnifythelength , 1 :Divide this leng p p p a p a p a p a Step1 Step2 Step3 Step4 Step5 th into 10 equal parts.
  34. 34. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts. :Countaanda+1partsstartingfromp.Thesearepoints and 1 :Magnifythelength , 1 :Divide this leng p p p a p a p a p a Step1 Step2 Step3 Step4 Step5 th into 10 equal parts. :Countbpartsstartingfrom p aStep6
  35. 35. How to represent a terminating decimal (p.ab) on the number line through successive magnification? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Locatethepointponthenumberline. :Dividetheunitlength , 1 into10equalparts. :Countaanda+1partsstartingfromp.Thesearepoints and 1 :Magnifythelength , 1 :Divide this leng p p p a p a p a p a Step1 Step2 Step3 Step4 Step5 th into 10 equal parts. :Countbpartsstartingfrom :Thispointrepresents p a p ab Step6 Step7
  36. 36. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  37. 37. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x.Step1
  38. 38. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string.n n Step1 Step2
  39. 39. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string. :Let ength of the recurring string of digits. n n m l Step1 Step2 Step3
  40. 40. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string. :Let ength of the recurring string of digits. :Fin n n m l Step1 Step2 Step3 Step4 d10n x
  41. 41. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string. :Let ength of the recurring string of digits. :Fin n n m l Step1 Step2 Step3 Step4 d10 :Find10 n m n x xStep5
  42. 42. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string. :Let ength of the recurring string of digits. :Fin n n m l Step1 Step2 Step3 Step4 d10 :Find10 :Find10 10 n m n m n n x x x x Step5 Step6
  43. 43. How to write a recurring decimal as a ratio of integers? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Rational Numbers Learn Math for Free. Visit www.ganitgurooz.com :Assume the given number as x. :Let umber of digits to the right of the decimal that do not form a part of the recurring string. :Let ength of the recurring string of digits. :Fin n n m l Step1 Step2 Step3 Step4 d10 :Find10 :Find10 10 :Divide the integer you get by10 10 to get the required rational form of the number x. n m n m n n m n n x x x x Step5 Step6 Step7
  44. 44. How to Rationalize an irrational denominator? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Learn Math for Free. Visit www.ganitgurooz.com
  45. 45. How to Rationalize an irrational denominator? Class – IX,CBSE MB0901: The Number System Important Procedures Topic: Irrational Numbers Form of Denominator Rationalising Factor Denominator of Rationalised Form a a a a b a b 2 a b a b a b a b m a n b m a n b 2 2 m a n b Learn Math for Free. Visit www.ganitgurooz.com

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