Question
\begin{tabular}{l} Is \( -\frac{41}{83} \) rational or irrational? \\ Select Choice \\ \hline\end{tabular}
Ask by Sanders Turnbull. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( -\frac{41}{83} \) is a rational number.
Solution
\( -\frac{41}{83} \) is a **rational** number.
### Explanation:
A **rational number** is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \) of two integers, where the numerator \( a \) is an integer and the denominator \( b \) is a non-zero integer.
In this case:
- **Numerator (\( a \))**: -41 (an integer)
- **Denominator (\( b \))**: 83 (a non-zero integer)
Since both the numerator and denominator are integers and the denominator is not zero, \( -\frac{41}{83} \) qualifies as a rational number.
### Conclusion:
**Rational**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To determine if \( -\frac{41}{83} \) is rational or irrational, one must know that rational numbers can be expressed in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Since both \(-41\) and \(83\) are integers, and \(83\) is not zero, \( -\frac{41}{83} \) is indeed a rational number. Rational numbers can be represented as fractions, but they can also be expressed as terminating or repeating decimals. For example, if you convert \(-\frac{41}{83}\) into decimal form, you'll get a repeating decimal that starts off as approximately \(-0.4937\ldots\). This shows yet another view of how rational numbers behave!
