Question

solutions of this question
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Answer 1

Answer:

below the answer is

Step-by-step explanation:

Answer:

x =o.777...= \frac{7}{9}x=o.777...=

9

7

(\frac{p}{q} \: form )(

q

p

form)

Step-by-step explanation:

Let x = 0.777...---(1)

Multiply equation (1) by 10, we get

=> 10x = 7.777....---(2)

Subtract equation (1) from equation (2) , we get

=> 9x = 7

x = \frac{7}{9}x=

9

7

(\frac{p}{q} \: form )(

q

p

form)

Therefore,

x =o.777...= \frac{7}{9}x=o.777...=

9

7

Answer 2

Answer:

$\textcircled{1}$

1. 3/15 = 0.2 => terminating form

$2. \ 2/11 = 0.181818... = 0.\overline{18} => \text{non-terminating recurring form}$

3. 329/400 = 0.8225 => terminating form

$4. \ 4/3 = 1.33333... = 1.\dot{3} => \text {non terminating recurring form}$

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$\textcircled{2}$

$\mathbf{1}. \ 0.0\overline7\\\text {Ans. Let x be 0.0 \overline7 }\\x = 0.0\overline7\\10x = 0.\overline7\\100x = 7.\overline7\\Now,\\100x - 10x = 7.\overline7 - 0.\overline7\\=> 90x = 7\\=> x = \frac{7}{90}\\\\\therefore 0.0\overline7 = \frac{7}{90}$

____________

$\mathbf{2.} \ 0.002\\\text{Ans. Multiplying and dividing by 1000, we get}\\\\0.002 = \frac{0.002 \times 1000}{1000} \\\\=> 0.002 = \frac{2}{1000} = \frac{1}{500}$

____________

$\mathbf{3.} \ 0.4\overline7\\\text{Ans. Let x be 0.4 \overline7 }\\10x = 4.\overline7\\100x = 47.\overline7\\=> 100x - 10x = 47.\overline7 - 4.\overline7\\=> 90x = 43\\=> x = \frac{43}{90}\\\\=> 0.4\overline7 = \frac{43}{90}$

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$\textcircled{3}$

$1. \sqrt{49} = 7=> \text{Rational Number}\\2. \sqrt{225} = 15 => \text{Rational number}\\3. \sqrt{24} = 4.89897948557... => \text{Irrational number}\\4. \sqrt{1024} = 32 => \text{Rational number}$

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