Question

answer me please Correct answer​

Answer 1

Answer

(i)  ²/₃

(ii)  ⁴³/₉₀

$\orange{\bigstar}$  Given  $\green{\bigstar}$

$\rm (i)\ 0.\bar{6}\\\\\rm (ii)\ 0.4\bar{7}$

$\orange{\bigstar}$  To Find  $\green{\bigstar}$

$\bullet \; \; \rm \dfrac{p}{q}\ form\ of\ given\ values$

$\orange{\bigstar}$  Solution  $\green{\bigstar}$

(i)

Let , x = 0.666... ___(1)

Multiply both sides of eq. (1) by 10 ,

⇒ 10x = 6.666... ___(2)

Now , Solve (2) - (1) ,

⇒ 10x - x = 6.666... - 0.666...

⇒ 9x = 6

⇒ x = $\rm \dfrac{6}{9}$

⇒ x = $\rm \dfrac{2}{3}$

_________________________

(ii)

Let , x = 0.4777...

Multiply both sides of the eq. by 10 ,

⇒ 10x = 4.777... ___(1)

Now , Again Multiply both sides of the equation by 10 ,

⇒ 100x = 47.777... ___(2)

Now , solve (2) - (1) ,

⇒ 100x - 10x = 47.777... - 4.777...

⇒ 90x = 43

⇒ x = $\rm \dfrac{43}{90}$

_________________________

Answer 2

Answer:

1.

$\frac{2}{3}$

2.

$\frac{43}{90}$