Given the number:
[tex]71.\bar{5186}[/tex]You can identify that there is a line about the first four decimal digits. That indicates that is a Repeating Decimal or Recurring Decimals.
Repeating Decimals are defined as those numbers whose decimal part becomes periodic.
By definition, Rational Numbers are those numbers that can be written as a simple fraction whose numerator and denominator are both integers.
By definition, Repeating Decimals are Rational Numbers.
Hence, the answer is: It is a Rational Number.