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**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.

∴ OA^{2} + AB^{2 }= OB^{2}

or 1^{2} + 1^{2} = OB^{2}

or 2 = OB^{2 }

⇒ 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.

∴ OA

or 1

⇒ OB = Again, draw BC ⊥ OB and cut off BC = 1 unit. Join OC.

Now, OBC is a right triangle.

∴ OB

or ()

or 2 + 1 = OC

⇒ OC = With centre as O and radius as OC draw an arc to intersect OX at D. Thus, OD = .

∴ 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 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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