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 ${\displaystyle \frac{p}{q}}$ 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.
$\begin{array}{rl}& r_1={\displaystyle \frac{1}{6}}\times (-1)={\displaystyle \frac{-1}{6}}\\ & r_2={\displaystyle \frac{2}{6}}\times (-1)={\displaystyle \frac{-2}{6}}\\ & r_3={\displaystyle \frac{3}{6}}\times (-1)={\displaystyle \frac{-3}{6}}\\ & r_4={\displaystyle \frac{4}{6}}\times (-1)={\displaystyle \frac{-4}{6}}\\ & r_5={\displaystyle \frac{5}{6}}\times (-1)={\displaystyle \frac{-5}{6}}\end{array}$
Thus, we obtain the answer of this questions to be the five numbers ${\displaystyle \frac{-1}{6}},{\displaystyle \frac{-2}{6}},{\displaystyle \frac{-3}{6}},{\displaystyle \frac{-4}{6}},{\displaystyle \frac{-5}{6}}$.

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 $r_6={\displaystyle \frac{-1}{6}}\times 6=-1$ 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.