Question Number 157813 by MathsFan last updated on 28/Oct/21
$${express}\:\:\mathrm{5}.\mathrm{1}\overset{\bullet} {\mathrm{3}}\overset{\bullet} {\mathrm{4}}\overset{\bullet} {\mathrm{5}}\:\:\:{into}\:{fraction} \\ $$
Answered by Rasheed.Sindhi last updated on 28/Oct/21
$${x}=\mathrm{5}.\mathrm{1}\overline {\mathrm{345}} \\ $$$$\mathrm{10}{x}=\mathrm{51}.\overline {\mathrm{345}}.................\left({i}\right) \\ $$$$\mathrm{10000}{x}=\mathrm{51345}.\overline {\mathrm{345}}.....\left({ii}\right) \\ $$$$\left({ii}\right)−\left({i}\right):\mathrm{9990}{x}=\mathrm{51345}−\mathrm{51} \\ $$$$\:\:\:\:{x}=\frac{\mathrm{51294}}{\mathrm{9990}}=\frac{\mathrm{8549}}{\mathrm{1665}}=\mathrm{5}\frac{\mathrm{224}}{\mathrm{1665}} \\ $$
Commented by MathsFan last updated on 28/Oct/21
$$\:{thank}\:{you} \\ $$
Answered by MJS_new last updated on 28/Oct/21
$$\mathrm{5}.\mathrm{1}\overline {\mathrm{345}}==\frac{\mathrm{1}}{\mathrm{10}}×\mathrm{51}.\overline {\mathrm{345}}=\frac{\mathrm{1}}{\mathrm{10}}\left(\mathrm{51}+\frac{\mathrm{345}}{\mathrm{999}}\right)= \\ $$$$=\frac{\mathrm{1}}{\mathrm{10}}×\frac{\mathrm{17098}}{\mathrm{333}}=\frac{\mathrm{8549}}{\mathrm{1665}} \\ $$