Question Number 12189 by tawa last updated on 16/Apr/17
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{to}\:\mathrm{the}\:\mathrm{below}\:\mathrm{deimal} \\ $$$$\mathrm{4}.\mathrm{4444444444444}.......\:\infty \\ $$
Answered by ridwan balatif last updated on 16/Apr/17
$$\mathrm{let}:\:\mathrm{4}.\mathrm{444444}...=\mathrm{a} \\ $$$$\mathrm{4}.\mathrm{4444}...=\mathrm{a} \\ $$$$−−−−−−−×\mathrm{10} \\ $$$$\mathrm{44}.\mathrm{4444}...=\mathrm{10a} \\ $$$$\mathrm{40}+\mathrm{4}.\mathrm{4444}=\mathrm{10a} \\ $$$$\mathrm{40}+\mathrm{a}=\mathrm{10a} \\ $$$$\mathrm{40}=\mathrm{9a} \\ $$$$\mathrm{a}=\frac{\mathrm{40}}{\mathrm{9}} \\ $$$$\mathrm{a}=\mathrm{4}\frac{\mathrm{4}}{\mathrm{9}} \\ $$
Commented by tawa last updated on 16/Apr/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$