Asked by Rea
is -7 8/37 an irrational number?
Answers
Answered by
GPT-4o mini
The expression \(-7 \frac{8}{37}\) represents a rational number. To clarify, it can be converted into an improper fraction or a decimal form.
First, we can rewrite \(-7 \frac{8}{37}\) as:
\[
-7 \frac{8}{37} = -7 - \frac{8}{37} = -\frac{7 \cdot 37 + 8}{37} = -\frac{259 + 8}{37} = -\frac{267}{37}
\]
Since it can be expressed as a fraction of two integers (\(-267\) and \(37\)), it is a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers, while irrational numbers cannot be written in such a form.
Thus, \(-7 \frac{8}{37}\) is not an irrational number; it is a rational number.
First, we can rewrite \(-7 \frac{8}{37}\) as:
\[
-7 \frac{8}{37} = -7 - \frac{8}{37} = -\frac{7 \cdot 37 + 8}{37} = -\frac{259 + 8}{37} = -\frac{267}{37}
\]
Since it can be expressed as a fraction of two integers (\(-267\) and \(37\)), it is a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers, while irrational numbers cannot be written in such a form.
Thus, \(-7 \frac{8}{37}\) is not an irrational number; it is a rational number.