Question

Find the $12$ rational number between $ - 1$ and $2$ ?

Answer 1

Hint: Here we will want a rational number we will have a number that can be expressed exactly by a ratio of two integers. So, we can convert numbers to rational format. And we will find the answer for the given question.

Complete step-by-step answer:
As we know rational numbers are in the format $\dfrac{p}{q}$ .
To find $12$ rational numbers between $ - 1$ and $2$ .
These numbers could also write as $\dfrac{{ - 1}}{1}$ and $\dfrac{2}{1}$ .
To find rational numbers we can make these numbers equivalent fractions.
So, this could be written as
By multiplying both the denominators and numerator by $10$ we get.
$\dfrac{{ - 10}}{{10}}$ and $\dfrac{{20}}{{10}}$
Now we can easily find the numbers
So, the numbers are
$\dfrac{1}{{10}},\dfrac{2}{{10}},\dfrac{3}{{10}},\dfrac{4}{{10}},\dfrac{5}{{10}},\dfrac{6}{{10}},\dfrac{7}{{10}},\dfrac{8}{{10}},\dfrac{9}{{10}},\dfrac{{10}}{{10}},\dfrac{{11}}{{10}},\dfrac{{12}}{{10}}$

Additional information:
A rational number is a number that can be expressed as the ratio of two integers. However, one third can be expressed as $1$ divided by $3$, and since $1$ and $3$ are both integers, one third is a rational number. Likewise, any integer can be expressed as the ratio of two integers, thus all integers are rational. Rational numbers together with addition and multiplication form a field which contains the integers, and is contained in any field containing the integers. In other words, the field of rational numbers is a prime field.

Note: Every integer is a rational number: for example, \[5\; = \;5/1.\]The decimal expansion of a rational number either terminates after a finite number of digits, or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.