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Convert-this-decimal-number-to-praction-number-1-0-3333-2-2-1111-3-0-1313-




Question Number 198954 by ArifinTanjung last updated on 26/Oct/23
 Convert this decimal number to     praction number  1. 0.3333... =...  2.  2.1111...=...  3. 0.1313....=...
$$\:\mathrm{Convert}\:\mathrm{this}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\:\:\mathrm{praction}\:\mathrm{number} \\ $$$$\mathrm{1}.\:\mathrm{0}.\mathrm{3333}…\:=… \\ $$$$\mathrm{2}.\:\:\mathrm{2}.\mathrm{1111}…=… \\ $$$$\mathrm{3}.\:\mathrm{0}.\mathrm{1313}….=… \\ $$
Answered by Rasheed.Sindhi last updated on 26/Oct/23
(1)  x=0.333...      (i)  10x=3.333...   (ii)  (ii)−(i): 9x=3⇒x=(3/9)=(1/3)  (2)   x=2.111...      (i)        10x=21.111...   (ii)  (ii)−(i): 9x=19⇒x=((19)/9)  (3)      x=0.131313...     (i)    100x=13.131313...   (ii)  (ii)−(i):  99x=13⇒x=((13)/(99))
$$\left(\mathrm{1}\right) \\ $$$${x}=\mathrm{0}.\mathrm{333}…\:\:\:\:\:\:\left({i}\right) \\ $$$$\mathrm{10}{x}=\mathrm{3}.\mathrm{333}…\:\:\:\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):\:\mathrm{9}{x}=\mathrm{3}\Rightarrow{x}=\frac{\mathrm{3}}{\mathrm{9}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\left(\mathrm{2}\right)\: \\ $$$${x}=\mathrm{2}.\mathrm{111}…\:\:\:\:\:\:\left({i}\right) \\ $$$$\:\:\:\:\:\:\mathrm{10}{x}=\mathrm{21}.\mathrm{111}…\:\:\:\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):\:\mathrm{9}{x}=\mathrm{19}\Rightarrow{x}=\frac{\mathrm{19}}{\mathrm{9}} \\ $$$$\left(\mathrm{3}\right) \\ $$$$\:\:\:\:{x}=\mathrm{0}.\mathrm{131313}…\:\:\:\:\:\left({i}\right) \\ $$$$\:\:\mathrm{100}{x}=\mathrm{13}.\mathrm{131313}…\:\:\:\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):\:\:\mathrm{99}{x}=\mathrm{13}\Rightarrow{x}=\frac{\mathrm{13}}{\mathrm{99}} \\ $$

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