How to Plot and Understand Decimals Using a Number Line
What are Decimal Numbers?
In Mathematics, a decimal number is considered to be a more precise number when compared to whole numbers. It is an integral part of Mathematics and thus students must have an understanding of the question “What are decimal numbers?” A decimal number is divided into two parts, the whole number and the remaining fractional of the concerned number. All the decimal numbers are separated by a decimal point. For example, the number 1.25 where 1 is an integral part and 25 is the fractional part. It is also possible to have decimal numbers on number lines and not just whole numbers.
What is Decimal Representation?
After understanding the fundamental question of “What are decimal numbers?” Let us now dissect the question of “what is decimal representation?”
All the numbers can be represented in decimal format. A non-negative real number “r” can be used as a decimal representation by expressing in the form of a series, it is written as a sum.
r = \[\sum_{i=0}^{∞}\] bᵢ/10ᵢ
b0= a non-negative integer
b1, b2, b3…= digits of decimal representation which satisfies 0 ≤ bi ≤ 9.
The digits in the above-given sequence are finite where bi is assumed to be 0. Some people may make it infinite whereas they forbid the decimal representation and add a sequence of 9. This makes a distinctive representation where the limitation still permits the decimal representation of a non-negative real number.
Decimal representation defines a number and can be written as:
r = b0. b1 b2 b3…
Here, b0 is the integer part of r (not obligatory between 0 and 9)
b1, b2, b3... are r’s fractional part.
This is the answer to the question of “what is decimal representation?”
How to represent the decimals on the number line?
Representation of decimals on the number line is different as compared to a whole number.
A line is divided into two parts between 0 and 1 like shown below
[Image will be Uploaded Soon]
Here, the line has 0 at the start and 1 at the end. If we divide this into two parts, we obtain a decimal in between the numbers as seen in the line below
[Image will be Uploaded Soon]
When divided, 0.5 is obtained which is a decimal. 0 is an integral part whereas 5 is the fractional part, separated by a dot represented as (1-0)/2 = 0.5.
Decimal numbers on the number line can also be shown by dividing the line into 10 parts.
If you want to show the decimals between 8 and 9, then divide the line into 10 parts like 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, and 8.9.
[Image will be Uploaded Soon]
In the above-given picture analyzing decimals numbers on number line, after 3 lines, decimal 8.4 is shown.
In the same way, to show the decimal 8.45, divide the portion between 8.4 and 8.5 into 10 parts.
[Image will be Uploaded Soon]
Here, after 4 consecutive lines 8.45 is denoted.
Similarly, as you move forward for decimals with more fractional value, keep dividing the numbers into 10 equal parts. Also, can be negative as well which we will see in the examples given below.
[Image will be Uploaded Soon]
Decimal Representation on Number Line Example
Decimal numbers on number lines can be represented in a positive as well as a negative value.
1. Show 0.3, 0.7, -0.4 and -1.2 decimal numbers on number lines.
Because, 0.3 = 3/10, 0.7 = 7/10, -0.4 = -4/10 and -1.2 = -12/10
As the above-mentioned representation of decimals on the number line, divide your line into ten equal parts that are the space between consecutive integers. The fraction 1/10 is represented by each part that is obtained.
[Image will be Uploaded Soon]
To point 0.3; shift three parts on the right-side of zero.
To point 0.7; shift seven parts on the right-side of zero.
To point -0.4; shift four parts on the left-side of zero
To point -1.2; shift twelve parts on the left-side of zero.
In the below diagram, 0.3, 0.7, -0.4, and -1.2 are denoted on a number line.
[Image will be Uploaded Soon]
Hence, it is possible to denote fractions and decimals on the number line if you understood how it must be done and how to divide the numbers properly. While plotting a decimal number make sure you count the lines properly so there are no errors.
FAQs on Decimal Representation on a Number Line Made Easy
1. What is the basic method for representing a decimal on a number line?
To represent a decimal on a number line, you first draw a line and mark the integers (e.g., 0, 1, 2, 3). Then, identify the two whole numbers the decimal lies between. For example, the decimal 2.6 lies between 2 and 3. You then divide the segment between these two integers into ten equal parts. Each part represents a tenth. The sixth mark after 2 would represent 2.6.
2. Can you give a simple example of how to plot a decimal like 0.7 on a number line?
Certainly. To plot 0.7, follow these steps:
Draw a number line and mark the points 0 and 1.
Divide the space between 0 and 1 into 10 equal sections.
Each section represents a tenth (0.1, 0.2, etc.).
Count seven sections to the right of 0. This point is the location of 0.7.
3. How is a decimal with multiple places, like 3.45, represented on a number line? Does it require a special technique?
Yes, representing decimals with hundredths or thousandths uses a technique called successive magnification. To plot 3.45:
First, locate the interval between 3 and 4. Divide it into tenths to find 3.4 and 3.5.
Next, 'zoom in' or magnify the space between 3.4 and 3.5.
Divide this magnified segment into another 10 equal parts. These new parts represent the hundredths.
The fifth mark in this new section will represent 3.45 accurately.
4. What is the rule for plotting a negative decimal, for example, -1.8, on a number line?
Plotting a negative decimal is similar to plotting a positive one, but it is done on the left side of zero. To plot -1.8, you first locate the integers -1 and -2. Then, you divide the segment between them into 10 equal parts. Counting eight parts from -1 towards -2 (to the left) will give you the precise location of -1.8.
5. How does representing a decimal like 0.5 on a number line compare to representing its equivalent fraction, 1/2?
Both 0.5 and 1/2 represent the exact same point on the number line. Representing 0.5 involves dividing the segment from 0 to 1 into ten parts and choosing the fifth mark. Representing the fraction 1/2 involves dividing the same segment into two equal parts and choosing the first one. Both methods lead you to the point that is exactly halfway between 0 and 1, demonstrating that they are just different ways of expressing the same value.
6. What is the importance of understanding place value (tenths, hundredths) when representing decimals on a number line?
Understanding place value is fundamentally important because it dictates the level of precision for plotting. The tenths place tells you how many primary divisions to make between two whole numbers. The hundredths place tells you how to further subdivide each of those tenths. Without a clear understanding of place value, you wouldn't know how many times to magnify a section or where to accurately place a decimal like 4.72.
7. In what real-world scenarios is it useful to visualise decimals on a number line?
Visualising decimals on a number line helps in understanding and comparing values in many real-world applications. For instance:
Measurement: A tailor using a measuring tape to cut fabric at 15.5 inches is using a physical number line.
Temperature: A thermometer showing a body temperature of 37.8°C visually places the value between 37°C and 38°C.
Weight: A digital weighing scale showing 2.75 kg helps us see that the weight is between 2 kg and 3 kg, and specifically, three-quarters of the way to 3 kg.
