Representation of Whole Numbers on Number Line: Fractions, Decimals, Examples

Whole numbers on a number line refer to the representation of whole numbers on a number line. The number line can also be used to compare two whole numbers, helping us to determine which is greater or smaller. A number line is a method of visually expressing numbers on a straight line. A straight line is divided into several segments, each separated by a unit distance. We can readily determine the difference between two numbers and perform comparisons by expressing them on a number line. Also, a line on which numbers are marked at a uniform distance can also be defined.

On this page, let’s learn everything about the representation of the whole numbers on a number line. Read on to find more.

Representation of Whole Numbers

A number line is a diagram that depicts numbers in a straight line. It serves as a guide to compare and sort numbers. Any real number, including whole numbers and natural numbers, can be represented by it.

Let’s recall:

The whole number is a collection of numbers that includes all counting numbers \((1,2,3,4,5,6)\) as well as zero \((0)\). In contrast, the natural number is the collection of all counting numbers, i.e. \(1,2,3,4,5,6, \ldots \)

It’s easier to compare numbers when they’re written on a number line. As shown in the diagram above, the integers on the left side are smaller than the integers on the right side. \(0\) is less than \(1,-1\) is less than \(0,-2\) is less than \(-1\), etc.

Representation of Whole Numbers using Fractional Notation

Fractions go beyond whole numbers and integers in our number system. They aid in the precise representation of any decimal number. Understanding how fractions represent part of a whole requires understanding how fractions are represented on the number line.

A fraction is a number that is not a whole number (such as \(\frac{2}{3},\frac{3}{5}\) etc.), as we all know. Let’s look at how fractions are represented on a number line.

On the number line, we already know how to represent whole numbers. Consider the figure below, which shows the numerals \(0\) and \(1\) represented on a number line.

If we need to represent the fraction \(\frac{2}{3}\) on the number line, we must divide the line segment between \(0\) and \(1\) into three equal portions, with the first division representing the fraction \(\frac{1}{3}\), the second division representing \(\frac{2}{3}\) and so on.

As we can see, to depict a fraction on a number line, we must divide the line segment between two whole numbers into \(n\) equal parts, where \(n\) is the fraction’s denominator.

For instance, if we need to represent the fraction \(\frac{2}{5}\) and \(\frac{4}{5}\) on the number line, we must divide the line segment between \(0\) and \(1\) into five equal portions, with the first division representing the fraction \(\frac{1}{5}\), the second division representing \(\frac{2}{5}\) and so on.

Examples of Representation of Whole Numbers

The number line can also compare two whole numbers, enabling us to identify which of the two is larger or smaller.

Let’s draw a straight line and mark a point \({\rm{0}}\) on it to represent whole numbers on a number line. Mark points \(A,B,C,D,E,F,G,H,\) and so on the line to the right of \({\rm{0}}\) at equal distances.

Because \(O\) is equal to the whole number \(0,A,B,C,D,\) and so on correspond to the whole numbers \(1,2,3,4,\) etc.

The arrow marks on both ends show that the number line continues on both sides indefinitely.

Example: Represent the whole numbers \(4,7\) and \(11\) on the same number line.
Solution: Numbers on a line refers to the representation of whole numbers on a number line.
Here is the representation of the whole numbers \(4,7\) and \(11\) on the number line as follows:

Representation of Whole Numbers using Decimals

The whole number and fraction are expressed using the decimal number system. A decimal point is a dot placed between two integers in a group of numbers called a decimal. Integers or whole numbers are the numbers to the left of the decimal point, whereas decimal numbers are the numbers to the right of the decimal point.

When we represent decimals on a number line, we can see the intervals between two integers, which helps us understand the fundamental concept of decimal number formation. On a number line, we can divide the unit length between \(0\) and \(1\) into \(10\) equal parts to represent a decimal number.

Example: Represent \(0.6\) on a number line.
We know that \(0.6\) is more than zero but less than one. There are \(6\) tenths in it. Divide the unit length between \(0\) into \(1\) into \(10\) equal parts and take \(6\) parts as shown below:

Solved Examples on Representation of Whole Numbers on Number Line

Q.1. Represent the fraction \(\frac{{33}}{5}\) on the number line.
Ans: By converting \(\frac{{33}}{5}\) into the mixed fraction we get, \(\frac{{33}}{5} = 6\frac{3}{5}\) 
Here, we will start at number \(6\) and divide the section between \(6\) and \(7\) into \(5\) equal portions (since \(5\) is in the denominator). Our required fraction is the third division, as illustrated in the diagram.

Q.2. Represent \(9.4\) on a number line.
Ans: To represent \(9.4\) on a number line, divide the segment between \(9\) and \(10\) into ten equal parts.

The arrow indicates \(9.4\), which is four parts to the right of \(9\).

Q.3. Represent the whole numbers \(3,9\) and \(13\) on the same number line.
Ans: Numbers on a line refers to the representation of whole numbers on a number line. Here is the representation of the whole numbers \(3,9\) and \(13\) on the number line as follows:

Q.4. On a number line, represent the decimals \(1.5,-1.2,-0.6\), and \(1.2\).
Ans: Now \(1.5 = \frac{{15}}{{10}}, – 1.2 = \frac{{ – 12}}{{10}}, – 0.6 = \frac{{ – 6}}{{10}}\) and \(1.2 = \frac{{12}}{{10}}\).
In \(10\) equal pieces, divide the space between each pair of consecutive integers (on the number line). Each part will represent the fraction \(\frac{1}{{10}}\), or decimal \(0.1\), and the resulting number line will be in the form:
Move fifteen parts to the right of zero to mark \(1.5\).
Move twelve parts to the left of zero to mark \(-1.2\).
Move six parts to the left of zero to mark \(-0.6\).
To get the number \(1.2\), shift twelve parts to the right of zero.

Q.5. Represent the fractions \(\frac{3}{7}\) and \(\frac{5}{7}\) on the number line.
Ans: If we need to represent the fraction \(\frac{3}{7}\) and \(\frac{5}{7}\) on the number line, we must divide the line segment between \(0\) and \(1\) into seven equal portions, with the third division representing the fraction \(\frac{3}{7}\), the fifth division representing \(\frac{5}{7}\) on the number line as follows:

Summary

In this article, we learnt about the representation of whole numbers using fractional notation and decimals along with examples and solved examples on the representation of whole numbers on the number line.  Further in the section below, the FAQs on the representation of whole numbers on the number line has been covered.

The learning outcome of this article is that the representation of whole numbers on a number line helps us compare the numbers.

FAQs Representation of Whole Numbers on Number Line

Q.1. How are whole numbers represented?
Ans: The number line can also compare two whole numbers, enabling us to identify which of the two is larger or smaller.
We can draw a straight line and mark a point \(O\) on it to represent whole numbers on a number line. Mark points \(A,B,C,D,E,F,G,H,\) and so on the line to the right of \(O\) at equal distances. And mark \(O\) as \(0\).
Because \(O\) is equal to the whole number \(0,A,B,C,D,\) and so on correspond to the whole numbers \(1,2,3,4\) etc.

Q.2. What is number line representation?
Ans: A number line is a graph that depicts numbers in a straight line. This line compares integers that are evenly spaced on an infinite line that extends horizontally on both sides.

Q.3. How do you use number lines?
Ans: Comparing numbers is easier when they are written on a number line. The numerals on the left of the number line are smaller than the numbers on the right. Addition, subtraction, and multiplication can all be done on a number line. We always add by moving right, subtract by moving left, and multiply by skipping a count.

Q.4. What is a number line for class \(7\)?
Ans: Number lines are horizontal straight lines in which integers are arranged at equal intervals in mathematics. A number line can depict all the numbers in a sequence. This is th simple number line suitable for class \(7\).

Q.5. Which is the best way to represent a whole number?
Ans: The expanded form is another way to represent whole numbers. To express a number, this form involves the addition of place values. For example, if your age is \(14\), you would write \(10+4\) in the extended form to reflect your age.

Q.6. What is \(\frac{3}{4}\) on a number line?
Ans: If we need to represent the fraction \(\frac{3}{4}\) on the number line, we must divide the line segment between \(0\) and \(1\) into four equal portions, with the third division representing the fraction \(\frac{3}{4}\).

Study Representation of Real Numbers on Number Line

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