Question

1. Express 0.7(bar on 7) in form p/q form . 2.Express 0.235(bar on 235) in p/q form, where p and q are integers and q ≠ 0

Answer 1

$\mathbb{ SOLUTION }$ :

$\bf{1. \: Express\: 0.\bar{7} \: in\: form\: p/q.}$

Let,
x = 0.777..... ___(i)

On multiplying both sides of {eq.(i)} by 10, we get,

10x = 7.777..... ___(ii)

On subtracting {eq.(i)} from {eq.(ii)} , we get,

=> 10x - x = (7.777...) - (0.777...)

=> 9x = 7

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

Hence,
0.$\bar{7}$ = $\frac{7}{9}$

➖➖➖➖➖➖➖➖➖➖➖

$\bf{2. \: Express\: 0. \overline{235} \: in\: form\: p/q \: where \: p\:and\:q \: are\:integers \: and \:q}$≠0

Let,
x = 0.235235.... ___(i)

On multiplying both sides of {eq.(i)} by 1000,we get,

1000x = 235.235235.... ___(ii)

On subtracting {eq.(i)} from {eq.(ii)} , we get,

=> 1000x - x = (235.235...) - (0.235...)

=> 999x = 235

=> x = $\frac{235}{999}$

Hence,
0.$\overline{235}$ = $\frac{235}{999}$

Answer 2

Hey there !!

▶ Q.1 → Express $0. \bar7$ in the p/q form .

▶ Solution :-

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

[ multiply both side by 10 ] .

=> 10 × x = 10 × 0.777...

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

➡ Now, Substracte in equation (2) and (1), we get

=> 10x - x = 7.777 - 0.777 .

=> 9x = 7.

•°• x = $\boxed{ \boxed{ \bf \frac{7}{9} }}$

▶ Q.2 → Express $0. \overline{235}$ in the p/q form .

▶ Solution :-

Let x = 0.235235235.........(1) .

[ multiply both side by 1000 ] .

=> 1000 × x = 1000 × 0.235235235...

=> 1000x = 235.235235235...........(2) .

➡ Now, Substracte in equation (2) and (1), we get

=> 1000x - x = 235.235235235 - 0.235235235

=> 999x = 235.

•°• x = $\boxed{ \boxed{ \bf \frac{235}{999} }}$

✔✔ Hence, it is solved ✅✅.

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THANKS

#BeBrainly.