A number line is an effective way of visualizing numbers. You can compare numbers easily on a number line and also can perform the four basic arithmetic operations viz., addition, subtraction, multiplication, and division visually.
As you can visualize whole numbers and integers on a number line, similarly you can also visualize the decimals on the number line. In this article, you’ll learn how to represent decimals on number line.
Decimal Numbers On Number Lines
Representing decimals on a number line is very much similar to the representation of fractions. The gaps between each of the numbers ($0$, $1$, $2$, …) are divided into the required number of divisions representing the fractional part of the decimal number.
The number of divisions between any two adjacent whole numbers or integers is divided into
- $10$ equal divisions in the case we want to represent $1$ digit decimal numbers
- $100$ equal divisions in the case we want to represent $2$ digit decimal numbers
- $1000$ equal divisions in the case we want to represent $3$ digit decimal numbers
How to Represent Decimals on Number Line?
To represent decimals on number line, draw a number line similar to the one used to represent whole numbers (starting from $0$). Now depending on the number of digits in decimal places, divide each of the adjacent numbers into equal divisions.
Representing Decimals With One Decimal Place On Number Line
Decimal numbers with one decimal place i.e., having a tenth place for decimal position means that there are $10$ equal divisions between each of the adjacent whole numbers.
In the above figure, the space between the adjacent whole numbers i.e., $0$ & $1$ and $1$ & $2$ is divided into $10$ equal parts, each part representing a distance of $0.1$, i.e., ${\frac {1}{10}}^{th}$ of a number.
Between $0$ and $1$, the partitions represent $0.1$, $0.2$, $0.3$, …, $0.9$. Similarly between $1$ and $2$, the partitions represent $1.1$, $1.2$, $1.3$, …, $1.9$.
Note: After $0.9$ the next partition will be $1.0$ which is equal to $1$ and similarly, after $1.9$ the next partition will be $2.0$ which is equal to $2$.
Examples
Ex 1: Represent $0.7$ on a number line.
The first step is to draw a whole number line with numbers starting from $0$. Next, divide the space between each adjacent number into $10$ units.
Observe that the whole number part in $0.7$ is $0$, so starting from $0$ move up to $7$ steps. The $7^{th}$ point represents $0.7$.
Ex 2: Represent $1.5$ on a number line.
The first step is to draw a whole number line with numbers starting from $0$. Next, divide the space between each adjacent number into $10$ units.
The whole number part in $1.5$ is $1$, so starting from $1$ move up to $5$ steps. The $5^{th}$ point represents $1.5$.
Ex 3: Represent $2.3$ on a number line.
The first step is to draw a whole number line with numbers starting from $0$. Next, divide the space between each adjacent number into $10$ units.
The whole number part in $2.3$ is $2$, so starting from $2$ move up to $3$ steps. The $3^{rd}$ point represents $2.3$.
Representing Decimals With Two Decimal Places On Number Line
Decimal numbers with two decimal places i.e., having up to the hundredth place for decimal position means that there are $100$ equal divisions between each of the adjacent whole numbers.
A division of $100$ between two adjacent whole numbers can be visualized as $10$ equal smaller divisions between two adjacent tenths, i.e., between $0.1$ & $0.2$ or $0.2$ & $0.3$ or $0.3$ & $0.4$, so on.
In the above figure, first of all, the whole number line is divided into $10$ equal parts to represent the tenth place of a decimal number.
The hundredth part of a decimal means dividing each of the tenths again into $10$ equal parts, as shown in the above figure. The line segment showed separately represents a distance between $0.1$ and $0.2$ divided into $10$ equal parts. Each of the equal divisions in the segment represents the hundredth part of a whole number. Hence, the partitions between $0.1$ and $0.2$ are $0.11$, $0.12$, $0.13$, …, $0.19$.
Note: After $0.19$ the next partition will be $0.20$ which is equal to $0.2$.
Examples
Ex 1: Represent $0.14$ on a number line.
The first step is to draw a whole number line with numbers starting from $0$. Next, divide the space between each adjacent number into $10$ units.
The whole part of the number is $0$. Therefore, consider the partitions between $0$ and $1$.
Now, observe that the digit at the tenth position is $1$, so divide the distance between $0.1$ and $0.2$ into $10$ equal parts.
Now, starting from $0.1$ move $4$ points. The $4^{th}$ point from $0.1$ represents $0.14$.
Ex 2: Represent $1.47$ on a number line.
The first step is to draw a whole number line with numbers starting from $0$. Next, divide the space between each adjacent number into $10$ units.
The whole part of the number is $1$. Therefore, consider the partitions between $1$ and $2$.
Now, observe that the digit at the tenth position is $4$, so divide the distance between $1.4$ and $1.5$ into $10$ equal parts. The $7^{th}$ point from $1.4$ represents $1.47$.
Representing Decimals With Three Decimal Places On Number Line
Decimal numbers with three decimal places i.e., having up to the thousandth place for decimal position means that there are $1000$ equal divisions between each of the adjacent whole numbers.
This can be visualized by further dividing the distance between each hundredth part into $10$ equal divisions. It means that there will be $10$ equal divisions between each of the distances of $0.11$ & $.12$, and $0.12$ & $0.13$, and so on.
In the above figure, first of all, the whole number line is divided into $10$ equal parts to represent the tenth place of a decimal number. Then each of the tenths is divided into $10$ equal parts to represent the hundredth part as shown by a line segment above the number line.
The thousandth part of a decimal means dividing each of the hundreds again into $10$ equal parts, as shown in the line segment below the number line. The distance between $0.11$ and $0.12$ is divided into $10$ equal parts, each part representing ${\frac {1}{1000}}^{th}$ of a whole number.
The line segment (below the number line) represents a distance between $0.11$ and $0.12$ divided into $10$ equal parts. Each of the equal divisions in the segment represents the thousandth part of a whole number. Hence, the partitions between $0.11$ and $0.12$ are $0.111$, $0.112$, $0.113$, …, $0.119$.
Note: After $0.119$ the next partition will be $0.120$ which is equal to $0.12$.
To represent negative decimals on a number line, draw a number line similar to the one used to represent whole numbers but here $0$ will be placed at the rightmost corner of the line. Now moving towards left from $0$ mark $-1$, $-2$, $-3$, … at equal intervals (these represent negative numbers, i.e., integers).
Next, divide the interval between each adjacent number into equal parts depending on the number of decimal places in the decimal number.
Practice Problems
Represent the following decimals on a number line.
- $0.6$
- $0.9$
- $1.4$
- $2.8$
- $0.35$
- $0.47$
- $1.38$
- $2.24$
FAQs
Can number lines have decimals?
Yes, a number line can be used to show the decimals. Since a decimal value represents a fractional part, the decimal numbers are represented by dividing the space between each whole number into equal parts.
How can you represent decimal numbers with one decimal place on a number line?
A decimal number with one decimal place represents the tenth for the fractional part. In order to represent such numbers on a number line, divide the space between each whole number into $10$ equal spaces.
For example to locate $2.7$ on a number line, divide the space between each whole number into $10$ equal spaces (since the number of decimal places is $1$). Now locate the whole number $2$ and move $7$ points from the number $2$. This point represents the decimal number $2.7$ on the number line.
How can you represent decimal numbers with two decimal places on a number line?
A decimal number with two decimal places represents the hundredth for the fractional part. In order to represent such numbers on a number line, divide the space between each whole number into $100$ equal spaces.
For example to locate $1.56$ on a number line, divide the space between each whole number into $100$ equal spaces (since the number of decimal places is $2$). Now locate the whole number $1$ and move $56$ points from the number $1$. This point represents the decimal number $1.56$ on the number line.
How do you locate negative decimals on a number line?
Locating negative decimals on a number line is very similar to locating positive decimals. The only difference is that we move towards the left-hand side of $0$ (zero) on the number line for negative decimals.
For example, to locate $-0.8$ on the number line, we mark the integers $0$ and $-1$, followed by making $10$ divisions and moving $8$ steps toward the left starting with $0$ as the reference point.
Conclusion
The procedure to represent decimals on number line is the same as that of whole numbers. In the case of decimal numbers, the adjacent whole numbers are divided into $10$ equal parts to represent tenths. Each of the tenths is further divided into $10$ equal intervals to represent hundredths. And further, each of the hundredths is divided into $10$ equal intervals.
