Question Number 6419 by sanusihammed last updated on 26/Jun/16
$${Convert}\:\:\:\:\mathrm{34}.\mathrm{8989898989}\:\:\:\:{and}\:\:\:\:\mathrm{0}.\mathrm{789789789789}\: \\ $$$${to}\:{fraction}. \\ $$
Answered by Rasheed Soomro last updated on 26/Jun/16
$${Do}\:{you}\:{mean}\:\:\mathrm{34}.\mathrm{8989898989}…\:\mathrm{89}\:{forever} \\ $$$${and}\:\mathrm{0}.\mathrm{789789789789}…\mathrm{789}\:{forever}? \\ $$$$ \\ $$$${Let}\:\:{x}=\mathrm{34}.\mathrm{8989898989}…\:\:\:\left({i}\right) \\ $$$$\:\:\:\:\:\mathrm{100}{x}=\mathrm{3489}.\mathrm{89898989}…\:\:\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right)\:\mathrm{99}{x}=\mathrm{3455} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{3455}}{\mathrm{99}}=\mathrm{34}\frac{\mathrm{89}}{\mathrm{99}} \\ $$$$ \\ $$$${Let}\:{x}=\mathrm{0}.\mathrm{789789789789}…\:\:\:\left({iii}\right) \\ $$$$\:\:\:\:\mathrm{1000}{x}=\mathrm{789}.\mathrm{789789789}…\:\:\:\left({iv}\right) \\ $$$$\left({iv}\right)−\left({iii}\right)\:\:\mathrm{999}{x}=\mathrm{789} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\frac{\mathrm{789}}{\mathrm{999}}=\frac{\mathrm{263}}{\mathrm{333}} \\ $$
Commented by sanusihammed last updated on 26/Jun/16
$${Wow}\:\:{thanks} \\ $$