The given statement is false
Given that 5.676677666777... is a rational number because it is decimal that goes on forever with a pattern, we have to check whether the statement is true or false
When a decimal number could be a rational number?
A decimal number that is repeating is a rational number as it can be written as p/q , where q neq 0.
For example : 3.56555...., 4.454545....
5.676677666777...
Here the number has no repeated pattern as we can see after the decimal (first 67 then 6677 then 666777).
Therefore the given number is not a rational number
To learn more about rational numbers click here https://brainly.com/question/24540629
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