let a,b,c be three digits, then the rational number 0.cabcabcab... can be represented as

\frac{99 c + a b}{990}

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\frac{100 c + 10 a + b}{999}

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\frac{99 c + 10 a + b}{990}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{99 c + 10 b + c}{990}

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Solution

The correct option is A $\frac{99 c + a b}{990}$
Let $0. c a b c a b c a b . . . . = x$
$x = 0. c a b c a b . . . .$
$1000 x = c a b . c a b . c a b . . .$
$1000 x - x = c a b$
$⟹ 999 x = 100 c + 10 a + b$
$∴ x = \frac{100 c + 10 a + b}{999}$

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