Question

Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes in forever with a pattern. Is he correct. Why or why not?

Answer 1

Answer: Jeremy is not correct as the decimal has no pattern.

Explanation:

• A decimal number that is repeating is a rational number as it can be written as
  `\frac pq` , where
  `q\\eq0`.

For example : 3.56555...., 4.454545....

Given: Jeremy says that 5.676677666777...

Here the number has no repeated pattern as we can see after the decimal (first 67 then 6677 then 666777).

That means it is not rational.

So, Jeremy is not correct as the decimal has no pattern.