Use geometric series to express $0.555... = 0. ¯ ¯ ¯ 5$ as a rational number.

\frac{1}{5}

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\frac{5}{9}

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\frac{5}{99}

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None of these

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Solution

The correct option is B $\frac{5}{9}$
$0. ¯ ¯ ¯ 5 = 0.5555...$

$0. ¯ ¯ ¯ 5 = 0.5 + 0.05 + 0.005 + . . . \infty$

$0. ¯ ¯ ¯ 5 = \frac{5}{10} + \frac{5}{10^{2}} + \frac{5}{10^{3}} + . . . \infty$

This is an infinite $G . P$ with $a = \frac{5}{10}$ and $r = \frac{1}{10}$

$0. ¯ ¯ ¯ 5 = \frac{(\frac{5}{10})}{1 - (\frac{1}{10})} = \frac{5}{9}$

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Similar questions

0.1 ¯ ¯¯¯¯¯¯ ¯ 576

\frac{- 11}{9}

- 99

Find the sum of the following series :

(i) 5 + 55 + 555 + ... to n terms.

(ii) 7 + 77 + 777 + ... to n terms.

(iii) 9 + 99 + 9999 + ... to n terms.

(iv) 0.5 + 0.55 + 0.555 + ... to n terms.

(v) 0.6 + 0.66 + 0.666 + ... to n terms.

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

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