We have seen that the repeating block of 1/7 is a cyclic number. Try to find more numbers (n) whose reciprocals (1/n) produce decimals with repeating blocks that are cyclic.

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TextRecurring and Non-recurring Decimal Expansions

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You know that 1/7 = 0.1̄4̄2̄8̄5̄7̄. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of 1/7 carefully.]

TextRecurring and Non-recurring Decimal Expansions

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

TextRecurring and Non-recurring Decimal Expansions