change0-356-into-p-q-form-

Question Number 12861 by Gauri last updated on 04/May/17

c h a n g e 0.35 \bar{6} i n t o p / q f o r m

Answered by mrW1 last updated on 04/May/17

x = 0.35 \bar{6} = 0.356666666 \dots \dots

100 x = 35.66666666 \dots = 35 + 0.66666 \dots

y = 0.666666 \dots

10 y = 6 + 0.666666 \dots = 6 + y

9 y = 6

y = \frac{6}{9} = \frac{2}{3}

\Rightarrow 100 x = 35 + \frac{2}{3} = \frac{107}{3}

\Rightarrow 0.35 \overset{―}{6} = x = \frac{107}{300}

Answered by ajfour last updated on 04/May/17

x = 0.35 \bar{6}

10 x = 3.5 \bar{6} = 3.56 \bar{6}

9 x = 3.21 = \frac{321}{100}

3 x = \frac{107}{100} \Rightarrow x = \frac{107}{300} .

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