Question Number 12861 by Gauri last updated on 04/May/17
$${change}\mathrm{0}.\mathrm{35}\overset{−} {\mathrm{6}}\:{into}\:{p}/{q}\:{form} \\ $$$$ \\ $$
Answered by mrW1 last updated on 04/May/17
$${x}=\mathrm{0}.\mathrm{35}\bar {\mathrm{6}}=\mathrm{0}.\mathrm{356666666}...... \\ $$$$\mathrm{100}{x}=\mathrm{35}.\mathrm{66666666}...=\mathrm{35}+\mathrm{0}.\mathrm{66666}... \\ $$$${y}=\mathrm{0}.\mathrm{666666}... \\ $$$$\mathrm{10}{y}=\mathrm{6}+\mathrm{0}.\mathrm{666666}...=\mathrm{6}+{y} \\ $$$$\mathrm{9}{y}=\mathrm{6} \\ $$$${y}=\frac{\mathrm{6}}{\mathrm{9}}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{100}{x}=\mathrm{35}+\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{107}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{0}.\mathrm{35}\overline {\mathrm{6}}={x}=\frac{\mathrm{107}}{\mathrm{300}} \\ $$
Answered by ajfour last updated on 04/May/17
$${x}=\mathrm{0}.\mathrm{35}\bar {\mathrm{6}} \\ $$$$\mathrm{10}{x}=\mathrm{3}.\mathrm{5}\bar {\mathrm{6}}=\mathrm{3}.\mathrm{56}\bar {\mathrm{6}} \\ $$$$\mathrm{9}{x}=\mathrm{3}.\mathrm{21}=\frac{\mathrm{321}}{\mathrm{100}} \\ $$$$\mathrm{3}{x}=\frac{\mathrm{107}}{\mathrm{100}}\:\Rightarrow\:{x}=\frac{\mathrm{107}}{\mathrm{300}}\:. \\ $$