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
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
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.
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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.
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.
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.
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.
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.