Representation of Decimals on Number Line: 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 numbers to the left of the decimal point, whereas decimal numbers are 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 divide the unit length between \(0\) and \(1\) into \(10\) equal parts to represent a decimal number. There are \(1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8,\) and \(1.9\) between any two integers, such as \(1\) and \(2.\) If we need to make a mark, we can use a ruler to mark between \(1\) and \(2.\)

Pictorial Representation of Decimals

Representation of tenths: Consider the following figure. It is divided into ten equal parts, and one part is shaded. The shaded part represents one-tenth of the whole figure. It is written as \(\frac{1}{{10}}.\frac{1}{{10}}\) is also written as \(0.1,\) which is read as ‘point one’ or ‘decimal one’.

Representation of hundredths: The figure below is divided into \(100\) equal parts, of which one part is shaded. The shaded part represents one-hundredth of the whole figure and is written as \(\frac{1}{{100}}.\frac{1}{{100}}\) is also written as \(0.01\) and is read as one-hundredth or point zero one or decimal zero one.

Now, let us look at what is the pictorial representation of \(23.5\)

That is, \(20 + 3 + \frac{5}{{10}} = 23.5\)

This is read as ‘twenty-three point five’.

Representation of Decimals on Number Line

Divide each number line segment into \(10\) equal segments to represent a decimal on a number line.

Example: Let us 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:

Visual Representation of Decimals

Suppose we want to locate \(2.665\) on the number line. We know that this lies between \(2\) and \(3.\)

So, let us look closely at the portion of the number line between \(2\) and \(3.\) Suppose we divide this into \(10\) equal parts and mark each division point as in the figure below. 

Then the first mark to the right of \(2\) will represent \(2.1,\) the second \(2.2,\) and so on. You might be finding some difficulty observing these points of division between \(2\) and \(3\) in the figure.

To have a clear view of the same, you may take a magnifying glass and look at the portion between \(2\) and \(3.\) It will look like what you see in the figure. Now, \(2.665\) lies between \(2.6\) and \(2.7.\) So, let us focus on the portion between \(2.6\) and \(2.7.\) in the figure. We imagine dividing this again into ten equal parts. The first mark will represent \(2.61,\) the next \(2.62,\) and so on. To see this clearly, we magnify this, as shown in the figure.

Again, \(2.665\) lies between \(2.66\) and \(2.67.\) So, let us focus on this portion of the number line and imagine dividing it again into ten equal parts. We magnify it to see it better, as in the figure. The first mark represents \(2.661,\) the next one represents \(2.662,\) and so on. So, \(2.665\) is the \({5^{{\rm{th}}}}\) mark in these subdivisions.

We call this process of visualisation of representation of numbers on the number line, through a magnifying glass, the process of successive magnification.

Representation of Repeating Decimals

Let’s try visualising a real number’s position (or representation) on the number line using a non-terminating recurring decimal expansion. We can visualise the position of the number on the number line by looking at appropriate intervals through a magnifying glass at successive magnifications.

Example: Visualise the representation of \(5.3\bar 7\) on the number line up to \(4\) decimal places, that is, up to \(5.3777.\)

Once again, we proceed by successive magnification and successively decrease the lengths of the portions of the number line in which \(5.3\bar 7\) is located. First, we see that \(5.3\bar 7\) is located between \(5\) and \(6.\) In the next step, we locate \(5.3\bar 7\) between \(5.3\) and \(5.4.\) To get a more accurate visualisation of the representation, we divide this portion of the number line into \(10\) equal parts and use a magnifying glass to visualise that \(5.3\bar 7\) lies between \(5.37\) and \(5.38.\) To visualise \(5.3\bar 7\) more accurately, we again divide the portion between \(5.37\) and \(5.38\) into ten equal parts and use a magnifying glass to visualise that \(5.3\bar 7\) lies between \(5.377\) and \(5.378.\) Now to visualise \(5.3\bar 7\) still, more accurately, we divide the portion between \(5.377\) and \(5.378\) into \(10\) equal parts and visualise the representation of \(5.3\bar 7\) as in the figure. Notice that \(5.3\bar 7\) is located closer to \(5.3778\) than to \(5.3777.\)

Solved Examples – Representation of Decimals on Number Line

Q.1. Take the help of the following figure to complete the table.

Shaded portions	Ordinary fraction	Decimal number
\(92\) squares

Ans: In the given figure, there are \(92\) squares shaded out of \(100\) squares.
So, we can write the ordinary fraction as \(\frac{{92}}{{100}}\) and the decimal number as \(0.92.\)
Therefore,

Shaded portions	Ordinary fraction	Decimal number
\(92\) squares	\(\frac{{92}}{{100}}\)	\(0.92\)

Q.2. Represent \(7.4\) on a number line.
Ans: To represent \(7.4\) on a number line, divide the segment between \(7\) and \(8\) into ten equal parts.

The arrow indicates \(7.4,\) which is four parts to the right of \(7.\)

Q.3. In the following illustration, write the decimal number that the arrow points to:

Ans: We need to write the decimal number that the arrow points to in the given figure.
The arrow is eight parts to the right of \(4.37.\) Then, the decimal number is \(4.378.\)
Therefore, \(4.378\) is the decimal number that the arrow points to in the given figure.

Q.4. On the number line, represent \(3.6.\)
Ans: The decimal number \(3.6=3+0.6\)
We begin at number \(3\) and divide the portion between \(3\) and \(4\) into ten equal parts on the number line. Taking six steps from \(3\) to \(4\) now gives us the representation of \(3.6.\)

Q.5. 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.

Summary

In this article, we learnt about the pictorial representation of decimals, representation of decimals on the number line, visual representation of decimals, representation of repeating decimals, solved examples on the representation of decimals on the number line, and FAQs on the representation of decimals on the number line.

The learning outcome of this article is the purpose of a decimal separator is to indicate the precision of a value.

FAQs – Representation of Decimals on Number Line

Q.1. What is a representation of a decimal number?
Ans: 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 divide the unit length between \(0\) and \(1\) into \(10\) equal parts to represent a decimal number. There are \(1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8,\) and \(1.9\) between any two integers, such as \(1\) and \(2.\) If we need to make a mark, we can use a ruler to mark between \(1\) and \(2.\)

Q.2. What is the decimal representation of seven hundredths?
Ans: The decimal equivalent of seven-hundredths is \(0.07.\)

Q.3. What is the difference between decimals and fractions?
Ans: On a number line, fractions and decimals are used to represent non-integers or partial numbers. Despite their similarities, there are several distinctions, such as fractions offering easier explanations of whole-number ratios. Fraction numbers result from dividing two numbers, with the numerator being the higher number and the denominator being the lower number. In contrast, decimal numbers are divided into two parts by a dot. \(2.25,\) for example, where \(2\) is the whole number and \(25\) represents the fractional half. We can convert decimals to integers and vice versa with ease.

Q.4. What is a decimal number?
Ans: A decimal number is defined as a decimal point separating the whole number and fractional parts. A decimal point is a dot in a decimal number. The digits after the decimal point represent a value less than one.

Q.5. What is a decimal number line?
Ans: Divide each number line segment into \(10\) equal segments to represent a decimal on a number line.

Learn about Decimal Numbers here

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