I have to prove that if n is any natural number then the decimal expansion of 1/n either terminates or repeats in blocks of numbers at most n-1 digits long.(adsbygoogle = window.adsbygoogle || []).push({});

for example, 1/11 = 0.0909090909... the repeating block of numbers is 09 which is 2 digits long and 2 is less than 11. 1/7 =0.142857142857142857...the repeating block of numbers is 142857 which is 6 digits long and 6 is less than 7. How do i prove that the size of the repeating block is ALWAYS less than the denominator whenever i divide by 1?

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# Repeating blocks of numbers?

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