Express 0.6+0.7bar + 0.47bar in the …

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Express 0.6+0.7bar + 0.47bar in the form of p/q

Posted by Rita Bishoyi 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

We have $0.6 = \frac{6}{{10}}$ ...(1)
Let $x = 0.\bar 7 = 0.777...$ ...(2)
Subtracting (1) from (2), we get
9x = 7 $\Rightarrow x = \frac{7}{9}$ or $0.\bar 7 = \frac{7}{9}$
Now, let $y = 0.4\bar 7 = 0.4777...$
$\therefore \;10y = 4.\bar 7$ ...(3)
And $100y = 47.\bar 7$ ...(4)
Subtracting (3) from (4), we get
90y = 43 $\Rightarrow y = \frac{{43}}{{90}}$
$\therefore \;0.4\bar 7 = \frac{{43}}{{90}}$
Now, $0.6 + 0.\bar 7 + 0.4\bar 7$ $= \frac{6}{{10}} + \frac{7}{9} + \frac{{43}}{{90}}$ $= \frac{{54 + 70 + 43}}{{90}} = \frac{{167}}{{90}}$
So, $\frac{{167}}{{90}}$ is of the form $\frac{p}{q}$ and $q \ne 0$ .

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