Is zero a rational number? Can you write it in the form \( \dfrac{p}{q} \) where \(p\) and \(q\) are integers and \(q \neq 0\)?
Yes. \(0 = \dfrac{0}{1} = \dfrac{0}{2} = \dfrac{0}{3}\) etc. The denominator \(q\) can also be taken as a negative integer.
Find six rational numbers between 3 and 4.
One method is to write: \(3 = \dfrac{21}{6+1}\) and \(4 = \dfrac{28}{6+1}\). The six rational numbers are \(\dfrac{22}{7}, \dfrac{23}{7}, \dfrac{24}{7}, \dfrac{25}{7}, \dfrac{26}{7}, \dfrac{27}{7}\).
Find five rational numbers between \( \dfrac{3}{5} \) and \( \dfrac{4}{5} \).
Since \( \dfrac{3}{5} = \dfrac{30}{50} \) and \( \dfrac{4}{5} = \dfrac{40}{50} \), five rational numbers between them are: \( \dfrac{31}{50}, \dfrac{32}{50}, \dfrac{33}{50}, \dfrac{34}{50}, \dfrac{35}{50} \).
State whether the following statements are true or false. Give reasons for your answers:
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
(i) True, since the collection of whole numbers contains all the natural numbers.
(ii) False, for example \(-2\) is not a whole number.
(iii) False, for example \(\dfrac{1}{2}\) is a rational number but not a whole number.