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Question Number 145393 by physicstutes last updated on 04/Jul/21

$$\mathrm{The}\mathrm{number}\frac{2}{13}\mathrm{expressed}\mathrm{as}\mathrm{a}\mathrm{decimal}\mathrm{is}0.153846153846...$$$$\mathrm{The}200\mathrm{th}\mathrm{and}300\mathrm{th}\mathrm{digits}\mathrm{are}?$$

Answered by mr W last updated on 04/Jul/21

$$mod(200,6)=2$$$$\Rightarrow 200thdigitis5$$$$mod(300,6)=0$$$$\Rightarrow 300thdigitis6$$

Answered by Olaf_Thorendsen last updated on 04/Jul/21

$$x=\frac{2}{13}=153846({10}^{-6}+{10}^{-12}+{10}^{-18}+...)$$$$$$$$200=6\times 33+2$$$$\mathrm{The}200\mathrm{th}\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{than}\mathrm{the}2\mathrm{nd}$$$$\mathrm{decimal}:5$$$$$$$$300=6\times 49+6$$$$\mathrm{The}300\mathrm{th}\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{than}\mathrm{the}6\mathrm{th}$$$$\mathrm{decimal}:6$$

Commented by physicstutes last updated on 04/Jul/21

$$\mathrm{thank}\mathrm{your}\mathrm{sirs}$$

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