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Question Number 6419 by sanusihammed last updated on 26/Jun/16

Convert 34.8989898989 and 0.789789789789 to fraction.

$${Convert}\:\:\:\:\mathrm{34}.\mathrm{8989898989}\:\:\:\:{and}\:\:\:\:\mathrm{0}.\mathrm{789789789789}\: \\ $$$${to}\:{fraction}. \\ $$

Answered by Rasheed Soomro last updated on 26/Jun/16

Do you mean 34.8989898989... 89 forever and 0.789789789789...789 forever? Let x=34.8989898989... (i) 100x=3489.89898989... (ii) (ii)−(i) 99x=3455 x=((3455)/(99))=34((89)/(99)) Let x=0.789789789789... (iii) 1000x=789.789789789... (iv) (iv)−(iii) 999x=789 x=((789)/(999))=((263)/(333))

$${Do}\:{you}\:{mean}\:\:\mathrm{34}.\mathrm{8989898989}...\:\mathrm{89}\:{forever} \\ $$$${and}\:\mathrm{0}.\mathrm{789789789789}...\mathrm{789}\:{forever}? \\ $$$$ \\ $$$${Let}\:\:{x}=\mathrm{34}.\mathrm{8989898989}...\:\:\:\left({i}\right) \\ $$$$\:\:\:\:\:\mathrm{100}{x}=\mathrm{3489}.\mathrm{89898989}...\:\:\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right)\:\mathrm{99}{x}=\mathrm{3455} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{3455}}{\mathrm{99}}=\mathrm{34}\frac{\mathrm{89}}{\mathrm{99}} \\ $$$$ \\ $$$${Let}\:{x}=\mathrm{0}.\mathrm{789789789789}...\:\:\:\left({iii}\right) \\ $$$$\:\:\:\:\mathrm{1000}{x}=\mathrm{789}.\mathrm{789789789}...\:\:\:\left({iv}\right) \\ $$$$\left({iv}\right)−\left({iii}\right)\:\:\mathrm{999}{x}=\mathrm{789} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{789}}{\mathrm{999}}=\frac{\mathrm{263}}{\mathrm{333}} \\ $$

Commented by sanusihammed last updated on 26/Jun/16

Wow thanks

$${Wow}\:\:{thanks} \\ $$

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