Question

Represents the rational number on a number line \[\dfrac{{ - 12}}{7}\].

Answer 1

Hint: Here in this question we have to represent the number on the number line. The given number is in the form of a rational number. So we write the numbers in the number line in the form of a rational number, then we can represent the given number on the number line.

Complete step by step answer:
In mathematics we have different kinds of numbers namely, natural number, whole number, integers, rational number, irrational number and real number. The rational number is defined or represented in the form of \[\dfrac{p}{q}\] where \[q \ne 0\] and p , q can be integers.

Number line: In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally. Usually in a number line the numbers will be represented in the form of integers. But here in this question we have to place a rational number on a number line.Now consider the given rational number.
\[ \Rightarrow \dfrac{{ - 12}}{7}\]

Between two numbers we can have any number of equal divisions. So now we consider
the number line where the points can be written in the form of rational. The number 0 can be written as \[\dfrac{0}{7}\] and the number 1 can be written as \[\dfrac{7}{7}\], the -1 can be written as \[\dfrac{{ - 7}}{7}\]. The number -2 can be written as \[\dfrac{{ - 14}}{7}\]. The given number is \[\dfrac{{ - 12}}{7}\], this number will comes in between the numbers \[\dfrac{{ - 7}}{7}\] and \[\dfrac{{ - 14}}{7}\].

So the number \[\dfrac{{ - 12}}{7}\] is represented on number is as shown below:

Note:We can convert the rational number into a decimal number, but here when we divide the number 12 by 7 we get a non terminating decimal number. So it is better to write the number line in the form of rational numbers. There can be any number of divisions but it should be partitioned equally.