Question Number 189350 by 073 last updated on 15/Mar/23
Answered by Rasheed.Sindhi last updated on 15/Mar/23
$$\mathrm{0}.\mathrm{7}\overline {\mathrm{9}}={y}\:\left({say}\right) \\ $$$$\mathrm{100}{y}=\mathrm{79}.\overline {\mathrm{9}} \\ $$$$\:\:\:\mathrm{10}{y}=\mathrm{7}.\overline {\mathrm{9}} \\ $$$$\mathrm{100}{y}−\mathrm{10}{y}=\mathrm{72} \\ $$$${y}=\frac{\mathrm{72}}{\mathrm{90}}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$${y}.{x}=\left(\frac{\mathrm{4}}{\mathrm{5}}×{x}\right)\:\in\mathbb{Z}^{+} \\ $$$${x}=\mathrm{5},\mathrm{10},\mathrm{15},… \\ $$$${Min}\left({x}\right)=\mathrm{5} \\ $$
Commented by 073 last updated on 15/Mar/23
$$\mathrm{nice}\:\mathrm{solution} \\ $$