Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Class 9: Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

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

Q1. Write four rational numbers equivalent to 5/7.

We have,
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Four rational numbers equivalent to 5/7 are 10/14, 15/21, 20/28, 25/35.


Q2. Find nine rational numbers between 0.1 and 0.2.

Let x = 0.1, y = 0.2 and n = 9.
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9The 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)
The nine rational numbers between 0.1 and 0.2 are 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 and 0.19.


Q3. Represent √2 on the number line (or on the real line).

  • 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 Notes | Study Mathematics (Maths) Class 9 - Class 9
  • 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'.


Q4. Represent √3 on the real line.

  • 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 Notes | Study Mathematics (Maths) Class 9 - Class 9
    ∵ 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'.


Q5. ExpressAdditional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 as a rational number in simplest form.

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
⇒ 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 Notes | Study Mathematics (Maths) Class 9 - Class 9


Q6. Express Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 in the form of Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9.

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
∴ 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 Notes | Study Mathematics (Maths) Class 9 - Class 9


Q7. Express Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 is the form of p/q in the simplest form.

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
∴ 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 Notes | Study Mathematics (Maths) Class 9 - Class 9


Q8. Find the sum of  (3√3 +7√2) and (√3 - 5√2)

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)


Q9. Divide 15 √12 by 3√3.

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q10. Rationalize the denominator ofAdditional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 (Prime factorize the numbers under the root in the denominator)
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q11. Rationalize the denominator of Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q12. If ‘a’ and ‘b’ are rational numbers and Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 find the values of ‘a’ and ‘b’.

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9              Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Comparing Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q13. If Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9, what is the value of x3 - 5x2 + 8x - 4? 

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
(x - 2)3 = x3 - 6x2 + 12x - 8 ...(1)
(x - 2)2 = x2 - 4x + 4 ... (2) 
(1) + (2) = x3 - 5x2 + 8x - 4 

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q14. Find the value of Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9 when Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9

Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
∵   Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9
Additional Question Answers: Number System Notes | Study Mathematics (Maths) Class 9 - Class 9


Q15. Rationalise the denominator of 1/[7+3√3].

1/(7 + 3√3)

By rationalizing the denominator,

= [1/(7 + 3√3)] [(7 – 3√3)/(7 – 3√3)]

= (7 – 3√3)/[(7)2 – (3√3)2]

= (7 – 3√3)/(49 – 27)

= (7 – 3√3)/22

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