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Express each of the following as a fraction in simplest form (1)0.365 recring on 65

Posted by Adarsh Anand 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have to express the given decimal in fractional form. So for that, let {tex}x = 0.3 \overline { 65 }{/tex}, then
x = 0.3656565.... ...(i)
10x = 3.656565.... ...(ii)
1000x = 365.656565.... ....(iii)
Subtracting (ii) from (iii), we obtain
{tex}990x = 362 \\ \Rightarrow x = \frac { 362 } { 990 } = \frac { 181 } { 495 }{/tex}

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