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Express 0.2545454............. As a fraction in …

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Express 0.2545454............. As a fraction in simplest form

Posted by Avantika Pandey 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let {tex}x = 0.2 \overline { 54 }{/tex} .
Then, x = 0.2545454... ...(i) ( multiply 10 on both sides)
{tex}\therefore{/tex} 10x = 2.545454... ...(ii)
and 1000x = 254.545454... ... (iii)
Subtract (ii) from (iii), we get
990x = 252 {tex}\Rightarrow x = \frac { 252 } { 990 } = \frac { 126 } { 495 } = \frac { 42 } { 165 } = \frac { 14 } { 55 }{/tex}.
{tex}\therefore \quad 0.2 \overline { 54 } = \frac { 14 } { 55 }{/tex}

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