Question

How do you graph \[\dfrac{1}{3}\] on a number line?

Answer 1

Hint: Here, we will graph the given number on the number line. We will find the decimal number for the given fraction and correct it to 4 decimal places. Then we will draw the number line and mark the decimal number on the line.

Complete step by step solution:
We are given a fraction \[\dfrac{1}{3}\].
Now, we will convert the given fractional number into a decimal number.
Let \[x\] be the given fraction number. So, we have \[x = \dfrac{1}{3}\].
Now, we will divide the numerator by the denominator of the given fraction to convert it into a decimal number. So, we get
\[ \Rightarrow x = 0.333....\]
\[ \Rightarrow x = 0.\overline 3 \]
Now, we will graph the number on a number line. So, we get

Therefore, the graph for the given number is represented on a number line.

Additional information:
We should know that the given number is a rational number since it is a non-terminating and recurring decimal. The bar over the decimal represents that the decimal is a recurring decimal. Recurring decimal is the repetition of decimal digits. Graphing a number on a number line is similar to the process of Visualization. This visualization is through successive magnification. We can visualize the representation of numbers on the number line by looking at a glimpse through a magnifying glass. The number line is a line similar only to \[x\]-axis with both the positive and negative integers.

Note:
We can also represent the fraction without converting the fraction into a decimal number. We should remember that the distance between two integers should be divided into the number of intervals as such the denominator. So, the interval is divided into 3 parts, since the denominator is 3. Thus, we will represent the number on a number line.