Question Number 36103 by mondodotto@gmail.com last updated on 28/May/18
$$\boldsymbol{\mathrm{convert}}\:\mathrm{0}.\mathrm{26999999}…\boldsymbol{\mathrm{into}}\:\boldsymbol{\mathrm{fraction}}\: \\ $$$$\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}\:\boldsymbol{\mathrm{where}}\:\boldsymbol{\mathrm{a}}\neq\mathrm{0} \\ $$
Answered by MJS last updated on 28/May/18
$$=\frac{\mathrm{26}}{\mathrm{100}}+\frac{\mathrm{9}}{\mathrm{900}}=\frac{\mathrm{27}}{\mathrm{100}} \\ $$
Commented by mondodotto@gmail.com last updated on 28/May/18
$$\mathrm{but}\:\mathrm{27}/\mathrm{100}\:\neq\mathrm{0}.\mathrm{26999999}… \\ $$$$\mathrm{why} \\ $$
Commented by MJS last updated on 29/May/18
$$\mathrm{3}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{3}×.\mathrm{333}…..=.\mathrm{999}…\:\mathrm{but}\:\mathrm{3}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{1}\:\Rightarrow \\ $$$$\Rightarrow\:.\mathrm{999}…=\mathrm{1} \\ $$
Answered by Rio Mike last updated on 28/May/18
$$\mathrm{round}\:\mathrm{up}\: \\ $$$$\mathrm{0}.\mathrm{27}\Rightarrow\:\frac{\mathrm{27}}{\mathrm{100}} \\ $$
Answered by Penguin last updated on 28/May/18
$${x}=\mathrm{0}.\mathrm{26999}… \\ $$$$\mathrm{100}{x}=\mathrm{26}.\mathrm{999}… \\ $$$$\mathrm{1000}{x}=\mathrm{269}.\mathrm{999}… \\ $$$$\mathrm{900}{x}=\mathrm{243} \\ $$$${x}=\frac{\mathrm{243}}{\mathrm{900}} \\ $$$${x}=\frac{\mathrm{27}}{\mathrm{100}} \\ $$