Additional Question Answers- Number System Class 9 Notes | EduRev

Mathematics (Maths) Class 9

Class 9 : Additional Question Answers- Number System Class 9 Notes | EduRev

The document Additional Question Answers- Number System Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9

Q.1. Write four rational numbers equivalent to 5/7.
Ans. We have,
Additional Question Answers- Number System Class 9 Notes | EduRev
► Four rational numbers equivalent to 5/7 are 10/14, 15/21, 20/28, 25/35.

Q.2. Find nine rational numbers between 0.1 and 0.2.
Ans. Let x = 0.1, y = 0.2 and n = 9.
Additional Question Answers- Number System Class 9 Notes | EduRevThe nine rational numbers between x and y are:
(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d), (x + 6d), (x + 7d), (x + 8d) and (x + 9d).
Nine rational numbers between 0.1 and 0.2 are:
(0.1 + 0.01); (0.1 + 0.02); (0.1 + 0.03); (0.1 + 0.04); (0.1 + 0.05); (0.1 + 0.06); (0.1 + 0.07); (0.1 + 0.08) and (0.1 + 0.09)
► 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 and 0.19.

Q.3. Represent √2 on the number line (or on the real line).
Ans. 

  • Draw XOX' and mark O as 0. 
  • Take OA = 1 unit.
  • Draw AB ⊥ OX and cut off AB = 1 unit.
    Additional Question Answers- Number System Class 9 Notes | EduRev
  • Now, OAB is a right triangle.
    ∵ OA2 + AB2 = OB2
    ► 12 + 12 = OB2
    ► 2 = OB2
    ► OB =√2 
  • With centre O and OB as radius, draw an arc intersecting OX at C.
  • Thus, OC = √2 on the real line XOX'.

Q.4. Represent √3 on the real line.
Ans. 

  • Draw XOX ' and mark O as 0 on it.
  • Take OA = 1 unit.
  • Draw AB ⊥ OX and cut off AB = 1 unit.
  • Join OB such that OAB is a right triangle.
    Additional Question Answers- Number System Class 9 Notes | EduRev
    ∵ OA2 + AB2 = OB2
    ► 12 + 12 = OB2
    ► OB =√2 
  • Again, draw BC ⊥ OB and cut off BC = 1 unit. Join OC.
  • Now, OBC is a right triangle.
    ∵ OB2 + BC2 = OC2
    ► √22 + 12 = OC2
    ► 2 + 1 = OB2
    ►  OC =√3
  • With centre as O and radius as OC draw an arc to intersect OX at D. 
  • Thus, OD =√3 on the real line XOX'.

Q.5. ExpressAdditional Question Answers- Number System Class 9 Notes | EduRev as a rational number in simplest form.
Ans.Additional Question Answers- Number System Class 9 Notes | EduRev
► 100x = 100 x (0.3838…)
► 100x = 38.3838...(2)
Subtracting (1) from (2),
We have, 100x – x = (38.3838…) – (0.3838…)
Additional Question Answers- Number System Class 9 Notes | EduRev

 Q.6. Express Additional Question Answers- Number System Class 9 Notes | EduRev in the form of Additional Question Answers- Number System Class 9 Notes | EduRev.
Ans.Additional Question Answers- Number System Class 9 Notes | EduRev
∴ 10x = 10 x (0.5353…)
or 10x = 5.333... ...(1)
Also, 100x = 53.333... ...(2)
Subtracting (1) from (2),
► 100x – 10x = (53.333…) – (5.333…)
► 90x = 48
Additional Question Answers- Number System Class 9 Notes | EduRev

Q.7. Express Additional Question Answers- Number System Class 9 Notes | EduRev is the form of p/q in the simplest form.
Ans.Additional Question Answers- Number System Class 9 Notes | EduRev
∴ 1000x = 1000 x (0.003003…)
or 1000x = 3.003003... …(2)
Subtracting (1) from (2),
We have 1000x – x = (3.003003…) – (0.003003…)
► 999x = 3
► x = 3/999 = 1/333
Thus,Additional Question Answers- Number System Class 9 Notes | EduRev

Q.8. Find the sum of  (3√3 +7√2) and (√3 - 5√2)
Ans. We have  (3√3 +7√2) + (√3 - 5√2)
= √3 3+7√2 + √3 - 5√2
= (3√3+√3) + 7√2 - 5√2)
= √3(3+1) + √2(7-2)
= √3(4) + √2(5) = (4√3 + 2√2)

Q.9. Divide 15 √12 by 3√3.
Ans.
Additional Question Answers- Number System Class 9 Notes | EduRev

Q.10. If ‘a’ and ‘b’ are rational numbers and Additional Question Answers- Number System Class 9 Notes | EduRev find the values of ‘a’ and ‘b’.
Ans.
Additional Question Answers- Number System Class 9 Notes | EduRev              Additional Question Answers- Number System Class 9 Notes | EduRev
Additional Question Answers- Number System Class 9 Notes | EduRev

Comparing Additional Question Answers- Number System Class 9 Notes | EduRev

Q.11. Find the value of Additional Question Answers- Number System Class 9 Notes | EduRev when Additional Question Answers- Number System Class 9 Notes | EduRev
Ans.
Additional Question Answers- Number System Class 9 Notes | EduRev
∵   Additional Question Answers- Number System Class 9 Notes | EduRevAdditional Question Answers- Number System Class 9 Notes | EduRevAdditional Question Answers- Number System Class 9 Notes | EduRev
Additional Question Answers- Number System Class 9 Notes | EduRev

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