Find whether 3/13 is rational or irrational without performing long division
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Step-by-Step Solution
Step 1: Understand Rational Numbers
A rational number is defined as any number that can be written as a fraction qp, 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 133. We need to determine if it fits the definition of a rational number.
Step 3: Check Conditions for Rationality
In the fraction 133, 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 133 can be expressed in the form qp where p=3 and q=13 are integers and q=0, it is a rational number.