Represent 0.585585….. In a rational form. Reverse the digits of the obtained fraction. Is is still recurring? [ 3 MARKS]

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Solution

Concept : 2 Marks
Calculation : 1 Mark

Let $x = 0. ¯ ¯¯¯¯¯¯ ¯ 585$

$1000 x = 585. ¯ ¯¯¯¯¯¯ ¯ 585$

$H e n c e 999 x = 585$

$x = \frac{585}{999}$

$x = \frac{95}{111}$

Once the digits are reversed, the fraction becomes: $\frac{59}{111}$ which is still recurring.

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Represent 0.585585….. In a rational form. Reverse the digits of the obtained fraction. Is is still recurring? [ 3 MARKS]

Concept : 2 Marks Calculation : 1 Mark Let x=0.¯¯¯¯¯¯¯¯585 1000x=585.¯¯¯¯¯¯¯¯585 Hence 999x=585 x=585999 x=95111 Once the digits are reversed, the fraction becomes: 59111 which is still recurring.

Concept : 2 Marks
Calculation : 1 Mark

Let $x = 0. ¯ ¯¯¯¯¯¯ ¯ 585$

$1000 x = 585. ¯ ¯¯¯¯¯¯ ¯ 585$

$H e n c e 999 x = 585$

$x = \frac{585}{999}$

$x = \frac{95}{111}$

Once the digits are reversed, the fraction becomes: $\frac{59}{111}$ which is still recurring.