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Question Number 57222 by Tawa1 last updated on 31/Mar/19

Express   5.27  in form of a series and show that is equal  to   5 (5/(18))

$$\mathrm{Express}\:\:\:\mathrm{5}.\mathrm{27}\:\:\mathrm{in}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\:\:\mathrm{5}\:\frac{\mathrm{5}}{\mathrm{18}} \\ $$

Answered by Joel578 last updated on 01/Apr/19

5.27^_  = 5.2 + (7/(10^2 )) + (7/(10^3 )) + (7/(10^4 )) + (7/(10^5 )) + ...              = ((52)/(10)) + ((7/(10^2 ))/(1 − (1/(10))))              = ((52)/(10)) + (7/(90))              = ((95)/(18)) = 5(5/(18))

$$\mathrm{5}.\mathrm{2}\overset{\_} {\mathrm{7}}\:=\:\mathrm{5}.\mathrm{2}\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{2}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{3}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{4}} }\:+\:\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{5}} }\:+\:... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{52}}{\mathrm{10}}\:+\:\frac{\frac{\mathrm{7}}{\mathrm{10}^{\mathrm{2}} }}{\mathrm{1}\:−\:\frac{\mathrm{1}}{\mathrm{10}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{52}}{\mathrm{10}}\:+\:\frac{\mathrm{7}}{\mathrm{90}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{95}}{\mathrm{18}}\:=\:\mathrm{5}\frac{\mathrm{5}}{\mathrm{18}} \\ $$

Commented by Tawa1 last updated on 01/Apr/19

God bless you sir

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$

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