Perform the long division for . Identify the repeating block of digits. Does it show cyclic properties if you evaluate ? Now compute , , etc. What do you notice?

Question

KnowledgeBoat · Accepted Answer

Performing long division for : ⇒ The repeating block is 076923 (6 digits). Computing other multiples of : Long division for : ⇒ Long division for : ⇒ Similarly, we have: ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ ⇒ Observations : 1\. The decimal expansions of form two distinct cyclic groups of 6 digits each, unlike which has one cyclic group. 2\. Group 1 : all share cyclic permutations of "076923". 3\. Group 2 : all share cyclic permutations of "153846". Hence, shows cyclic behaviour, but unlike , it produces two different cyclic blocks among its multiples.

Mathematics

Perform the long division for . Identify the repeating block of digits. Does it show cyclic properties if you evaluate ? Now compute , , etc. What do you notice?

Whole Numbers

Related Questions