We are given the number (3)/(13). We need to determine if it fits the definition of a rational number.

Since (3)/(13) can be expressed in the form (p)/(q) where p=3 and q=13 are integers and q ≠ 0, it is a rational number.

Find whether 3/13 is rational or irrational without performing long division

Answer: The number $\frac{3}{13}$ is a rational number.

Step-by-step solution

Step 1: Understand Rational Numbers

A rational number is defined as any number that can be written as a fraction $\frac{p}{q}$ , where $p$ and $q$ are integers, and $q$ is not equal to zero. This definition is fundamental to classifying numbers as rational or irrational.

Step 2: Analyze the Given Number

We are given the number $\frac{3}{13}$ . We need to determine if it fits the definition of a rational number.

Step 3: Check Conditions for Rationality

In the fraction $\frac{3}{13}$ , the numerator $p$ is $3$ , which is an integer. The denominator $q$ is $13$ , which is also an integer. Furthermore, the denominator $13$ is not equal to zero. All conditions for a rational number are met.

Step 4: Conclusion

Since $\frac{3}{13}$ can be expressed in the form $\frac{p}{q}$ where $p=3$ and $q=13$ are integers and $q \neq 0$ , it is a rational number.

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