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Question Number 427 by 9999 last updated on 25/Jan/15

How many digits are present in  periodic part for decimal expansion  of (1/7^(11) )?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{present}\:\mathrm{in} \\ $$$$\mathrm{periodic}\:\mathrm{part}\:\mathrm{for}\:\mathrm{decimal}\:\mathrm{expansion} \\ $$$$\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{11}} }? \\ $$

Commented by 123456 last updated on 02/Jan/15

10^n ≡1(mod7^(11) )

$$\mathrm{10}^{{n}} \equiv\mathrm{1}\left(\mathrm{mod7}^{\mathrm{11}} \right) \\ $$

Answered by prakash jain last updated on 02/Jan/15

6×7^(10)

$$\mathrm{6}×\mathrm{7}^{\mathrm{10}} \\ $$

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