Final answer:
13.4 is a rational number because it can be expressed as a fraction with integers (134/10). It is not a prime number, as prime numbers must be whole numbers greater than 1. It is also not an irrational number, as it does not have a non-repeating, non-terminating decimal expansion, nor is it an even number, which must be an integer divisible by 2. Option B is the correct answer.
Step-by-step explanation:
The question at hand is determining the nature of the number 13.4. To address this, we must evaluate 13.4 against several mathematical property categories: Prime number, Rational number, Irrational number, and Even number.
- Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Since 13.4 is not a whole number, it cannot be considered for primality.
- Rational number: A rational number is any number that can be expressed as the quotient or fraction of two integers, with the denominator not being zero. Since 13.4 can be written as 134/10, it is indeed a rational number.
- Irrational number: An irrational number is a number that cannot be expressed as a simple fraction. Rational numbers have finite or repeating decimal expansions, whereas irrational numbers have a non-repeating, non-terminating decimal expansion. Given that 13.4 has a terminating decimal expansion, it is not an irrational number.
- Even number: An even number is any integer that can be divided by 2 leaving no remainder. As 13.4 is not an integer, we cannot classify it as even or odd.
Based on these definitions, 13.4 can be categorized as a rational number, but it is not a prime number, an irrational number, or an even number. Therefore, the correct options are B. Rational number.