Question

List five rational numbers between -1 and 0.

Answer 1

Hint: In this question we have been asked to find 5 rational numbers between -1 and 0. Therefore, we should first understand what are rational numbers and then use it to find the required answer.

Complete step-by-step answer:
In this question, we are asked to find rational numbers in a given interval. Therefore, we should understand what rational numbers are first.
A number is said to be a rational number if it can be expressed in the form of $\dfrac{p}{q}$ where p and q are integers and $q\ne 0$……………………(1.1)

Considering equation (1.1), we note that, to find rational numbers between -1 and 0, we can find fractions of -1 which lie between -1 and 0. As, we have to find 5 numbers, we can divide -1 into 6 parts and each part will correspond to one rational number between -1 and 0.
$\begin{align}
  & {{r}_{1}}=\dfrac{1}{6}\times \left( -1 \right)=\dfrac{-1}{6} \\
 & {{r}_{2}}=\dfrac{2}{6}\times \left( -1 \right)=\dfrac{-2}{6} \\
 & {{r}_{3}}=\dfrac{3}{6}\times \left( -1 \right)=\dfrac{-3}{6} \\
 & {{r}_{4}}=\dfrac{4}{6}\times \left( -1 \right)=\dfrac{-4}{6} \\
 & {{r}_{5}}=\dfrac{5}{6}\times \left( -1 \right)=\dfrac{-5}{6} \\
\end{align}$
Thus, we obtain the answer of this questions to be the five numbers $\dfrac{-1}{6},\dfrac{-2}{6},\dfrac{-3}{6},\dfrac{-4}{6},\dfrac{-5}{6}$.

Note: We should note that to find five rational numbers, we had to divide -1 into 6 parts because the sixth part will be equal to ${{r}_{6}}=\dfrac{-1}{6}\times 6=-1$ which is equal to -1 and thus not strictly between -1 and 0. Also, one other method to find five rational numbers is to use the property that any number having non-recurring decimal representation is a rational number. Thus, the numbers ${{p}_{1}}=-1+0.1=-0.9$, ${{p}_{2}}=-1+0.01=-0.99$, ${{p}_{3}}=-1+0.001=-0.999$, ${{p}_{4}}=-1+0.0001=-0.9999$ and ${{p}_{1}}=-1+0.00001=-0.99999$ will also be valid answers to this question.