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Question Number 198954 by ArifinTanjung last updated on 26/Oct/23

$$\mathrm{Convert}\mathrm{this}\mathrm{decimal}\mathrm{number}\mathrm{to}$$$$\mathrm{praction}\mathrm{number}$$$$1.0.3333...=...$$$$2.2.1111...=...$$$$3.0.1313....=...$$

Answered by Rasheed.Sindhi last updated on 26/Oct/23

$$\left(1\right)$$$$x=0.333...\left(i\right)$$$$10x=3.333...\left(ii\right)$$$$\left(ii\right)-\left(i\right):9x=3\Rightarrow x=\frac{3}{9}=\frac{1}{3}$$$$\left(2\right)$$$$x=2.111...\left(i\right)$$$$10x=21.111...\left(ii\right)$$$$\left(ii\right)-\left(i\right):9x=19\Rightarrow x=\frac{19}{9}$$$$\left(3\right)$$$$x=0.131313...\left(i\right)$$$$100x=13.131313...\left(ii\right)$$$$\left(ii\right)-\left(i\right):99x=13\Rightarrow x=\frac{13}{99}$$

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