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

Get the complete, step-by-step math solution for: "Find whether 3/13 is rational or irrational without performing long division...". Powered by SolveForX AI math tutor.

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.