Question Number 57222 by Tawa1 last updated on 31/Mar/19
$$\mathrm{Express}\:\:\:\mathrm{5}.\mathrm{27}\:\:\mathrm{in}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\:\:\mathrm{5}\:\frac{\mathrm{5}}{\mathrm{18}} \\ $$
Answered by Joel578 last updated on 01/Apr/19
$$\mathrm{5}.\mathrm{2}\overset{\_} {\mathrm{7}}\:=\:\mathrm{5}.\mathrm{2}\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{2}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{3}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{4}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{5}} }\:+\:… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{52}}{\mathrm{10}}\:+\:\frac{\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{2}} }}{\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{10}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{52}}{\mathrm{10}}\:+\:\frac{\mathrm{7}}{\mathrm{90}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{95}}{\mathrm{18}}\:=\:\mathrm{5}\frac{\mathrm{5}}{\mathrm{18}} \\ $$
Commented by Tawa1 last updated on 01/Apr/19
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$