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## Mathematics (Maths) Class 9

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## 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

Ques 1. Write four rational numbers equivalent to 5/7
Solution: We have, ∵ Four rational numbers equivalent to Ques 2. Find nine rational numbers between 0.1 and 0.2.
Solution:
Let x = 0.1, y = 0.2 and n = 9 [∵ (0.2) > (0.1)] Since, the 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).
or 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18 and 0.19.

Ques 3: Represent on the number line (or on the real line).
Solution: Draw XOX' and mark O as 0. Take OA = 1 unit.
Draw AB ⊥ OX and cut off AB = 1 unit. Now, OAB is a right triangle.
∴ OA2 + AB= OB2
or 12 + 12 = OB2
or 2 = OB
⇒  OB = With centre O and OB as radius, draw an arc intersecting OX at C.
Thus, OC = on the real line XOX'.

Ques 4: Represent on the real line.
Solution:
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. ∴ OA2 + AB= OB2
or 12 + 12 = OB
⇒ OB = Again, draw BC ⊥ OB and cut off BC = 1 unit. Join OC.
Now, OBC is a right triangle.
∴ OB2 + BC2 = OC2
or ( )2 + (1)= OC2
or  2 + 1 = OC2
⇒ OC = With centre as O and radius as OC draw an arc to intersect OX at D. Thus, OD = .

Ques 5: Express 0. as a rational number in simplest form.
Solution: Let x = 0. 38 = 0.3838       ... ...(1)
∴ 100x = 100 x (0.3838…)
or 100x = 38.3838        ...(2)
Subtracting (1) from (2),
we have 100x – x = (38.3838…) – (0.3838…)
or 99x = 38 or x = Thus, 0. = Ques 6: Express in the form of .
Solution: Let x = = 0.5333…
∴ 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…)
or 90x = 48
or x = Thus, = Ques 7: Express is the form of p/q in the simplest form.
Solution: Let x = = 0.003003                 ... …(1)
∴ 1000x = 1000 x (0.003003…)
or 1000x = 3.003003               ... …(2)
Subtracting (1) from (2),
we have 1000x – x = (3.003003…) – (0.003003…)
or    999x = 3
or    x = 3/999 = 1/333
Thus Ques 8: Find the sum of  (3√3 +7√2) and (√3 - 5√2)
Solution :
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 + 5√2)

Ques 9: Divide 15 √12 by 3√3.
Solution: We have: Ques 10: If ‘a’ and ‘b’ are rational numbers and find the values of ‘a’ and ‘b’.
Solution: We have   Comparing Ques 11: Find the value of when Solution:     ,

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