# 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,

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.
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)
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.
• 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.

∵ 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. Express as a rational number in simplest form.

⇒ 100x = 100 x (0.3838…)
⇒ 100x = 38.3838...(2)
Subtracting (1) from (2),
We have, 100x – x = (38.3838…) – (0.3838…)

Q6. Express  in the form of .

∴ 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

Q7. Express  is the form of p/q in the simplest form.

∴ 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,

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.

Q10. Rationalize the denominator of

(Prime factorize the numbers under the root in the denominator)

Q11. Rationalize the denominator of

Q12. If ‘a’ and ‘b’ are rational numbers and  find the values of ‘a’ and ‘b’.

Comparing

Q13. If , what is the value of x3 - 5x2 + 8x - 4?

(x - 2)3 = x3 - 6x2 + 12x - 8 ...(1)
(x - 2)2 = x2 - 4x + 4 ... (2)
(1) + (2) = x3 - 5x2 + 8x - 4

Q14. Find the value of  when

∵

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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