Question

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

Answer 1

We need to find the number of digits in the recurring block of 1/17.

Let us perform the long division to get the recurring block of  ___. We need to divide 1 by 17, to get

We can observe that while dividing 1 by 17 we got the remainder as 1, which will continue to be 1 after carrying out 16 continuous divisions.

Therefore, we conclude that 1/17 = 0.0588235294117647..... or 1/17 = bar (0.0588235294117647), which is a non-terminating decimal and recurring decimal.