To solve the problem of identifying five rational numbers smaller than 5, let's first briefly revisit the definition of a rational number. A rational number is any number that can be expressed as the quotient or fraction of two integers, with a non-zero denominator. Essentially, it means that any number that can be written in the form [tex]\( \frac{p}{q} \)[/tex] where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers and [tex]\( q \)[/tex] is not zero is a rational number.
Given these definitions and requirements, we look for five specific rational numbers that are less than 5. Here are five such examples:
1. 4.5: This number can be written as [tex]\( \frac{9}{2} \)[/tex], which is a rational number because it is the quotient of the integers 9 and 2.
2. 3.75: This number can be written as [tex]\( \frac{15}{4} \)[/tex], another rational number as it represents the fraction of two integers, 15 and 4.
3. 2.5: This number can be written as [tex]\( \frac{5}{2} \)[/tex]. It is a rational number as it is the quotient of the integers 5 and 2.
4. 1.25: This number can be expressed as [tex]\( \frac{5}{4} \)[/tex], thereby making it a rational number since it is the quotient of 5 and 4.
5. 0.5: This number can be written as [tex]\( \frac{1}{2} \)[/tex], which is a rational number since it represents the fraction of the integers 1 and 2.
Hence, the five rational numbers smaller than 5 are:
1. 4.5
2. 3.75
3. 2.5
4. 1.25
5. 0.5
