To determine what type of number can be written as a fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex], let's understand the definitions of each of the given choices.
A. A rational number
- A rational number is any number that can be expressed as [tex]\(\frac{p}{q}\)[/tex] where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex]. For example, [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{5}{3}\)[/tex], and [tex]\(\frac{-4}{7}\)[/tex] are all rational numbers.
B. An irrational number
- An irrational number cannot be expressed as a fraction [tex]\(\frac{p}{q}\)[/tex]. It cannot be represented as a simple fraction where both [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers. Examples include [tex]\(\sqrt{2}\)[/tex] and [tex]\(\pi\)[/tex].
C. [tex]\(\pi\)[/tex]
- [tex]\(\pi\)[/tex] is a well-known irrational number and cannot be written as an exact fraction of two integers.
D. All numbers
- Not all numbers can be written as a fraction [tex]\(\frac{p}{q}\)[/tex]. For example, irrational numbers do not meet this criterion.
Given these definitions, the correct choice is:
A. A rational number
So, the type of number that can be written as a fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex], is a rational number.
