Question

express 0.57 bar in p/q

Answer 1

Answer:

( p/q form )

Explanation:

Let x = 0.575757.....---(1)

Multiply equation (1) by 100,we get

100x = 57.575757....---(2)

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

99x = 57



Write it in least form, we get





Therefore,

 ( p/q form )

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Answer 2

Answer:-

To:-

Express $0. \overline{57}$ in form of $\frac{p}{q}$ (Rational number).

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Let $(x)$ = $0. \overline{57}$

(Taken the non terminating recurring number as a desired alphabet.)

$\blue{ \therefore 100x = 57. \overline{57}}$

(Since recurring was on the tenths and the oneths place, 100 is multiplied with (x) so that the RHS also changes)

$\implies 100x = 57 + 0. \overline{57}$

(Separated the number with was in decimal form)

$\blue{ \implies 100x = 57 + x }$

[Remember? We had taken $0. \overline{57}$ as (x)]

$\implies 100x - x = 57$

(Taken the variable like terms in the LHS)

$\blue{ \implies 99x = 57}$

(Subtraction in the LHS)

${ \implies x = \frac{57}{99}}$

(Taken 9 to RHS)

$\blue{ \implies x = \frac{\cancel{57}}{\cancel{99}}}$

(Cancelled 57 and 99)

$\implies x = \frac{19}{33}$

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Required Answer:-

Therefore, $0. \overline{57}$ is 19/33.

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