Profile
Settings
Refer your friends
Sign out
With the help of the decimal system, we can easily express the part of a whole number and the part of a fraction by distinguishing it with a dot that is known as a decimal point. The concept of decimals enables us to convert any whole number into decimal form and vice versa.
To get a clear view of this concept of decimals, let’s take up an example, a geometry box costs 85 rupees and 50 paise. So now if we want to convert this sum of money into a single figure then we can just quote it as Rs. 85.50. So, the point that differentiates rupee from paise is the decimal.
Definition
The set of numerals that lie between the integers present on a line of numbers is called decimal. In view of mathematics, it is just a unique way of representing the link between fractions and decimals. The main role of decimals is to help in getting a more accurate value to write when measuring quantities like weight, money, distance, length, etc.
Understanding decimals
Considering a number line, let us take the decimal point on the centre of the line and its left side; all the numerals that are present are known as whole numbers or integers. While on the right side are the decimal fractions.
When we move on the right side from one place it is considered that the following place would be smaller, around 1/10 times in value. And this would be noted as the tenth or 1/10th place value.
Decimal and its types
The categorization of decimals can be done in three distinct ways which are based on the occurrence of different digit types after the point of the decimal. It will be based on the criteria of whether the figures are terminating, non-repeating or repeating.
For a brief idea we can refer to the following
Terminating decimals: In this, the decimal numbers are terminated after a fixed number of places of decimal and it does not repeat like for instance 564.565435, 87.6, etc.
non-terminating decimals: In this type, the decimal numerals have unlimited digits after the point of the decimal. 34534.8753458742…, 876.765768973…etc. can be the examples for this kind. This category is further split into two types:
Repeating decimals: In this, after the completion of a fixed internal, the digits are reoccurred. 98745.767676767…, 546.898989… etc can be examples of this type.
non-repeating decimals: Even after the fixed internal is completed, the digits never recurred. For example, 765.976382883…., 456.2387543…. etc.
Chart for Place Value
If we look at the scenario of decimals, taking the part of whole numerals, it is seen that the place value criteria are similar to the whole numeral itself. But there is a vast set of numbers that is being carried on after the point of the decimal and in this, we make use of decimal fractions for representation of the value and we can simply get to know the way of converting fractions to decimals.
It is noticed that when we move to the left side, the previous place value is ten times less than the present place value. Talking about the one’s place, on the right side we have 1/10 or tenths and moving right of the 1/10 we obtain 1/100 or hundredths and this series goes on.
Let’s comprehend this from an illustration, determining the place value of each figure of the numerals 89.737, 9.530, and 54.07. Now will understand the concept of decimal place value with the help of a table
Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
8 | 9 | . | 7 | 3 | 7 |
| 9 | . | 5 | 3 | 0 |
5 | 4 | . | 0 | 7 |
|
How to Read Decimals
There can certainly be two alternatives for reading decimal numerals. Using the first option we just need to easily read out the whole numeral which is followed by the “decimal point”. After this, the figures in the fractional part are to be read separately. By this, we can read the decimals more casually.
For instance, figure 78.56 can be read as seventy-eight point five-six.
The second alternative can be in a way that we read the part of the whole numeral and then add “and”. After this, we can jump to the part of fraction for reading as we did in the whole numeral part but in that the place value of the preceding figure was followed.
For instance, digit 87.65 can be interpreted as eighty-seven and sixty-five hundredths
Expanded Form of Decimals
Just like the way of writing whole numbers in the expanded system, the decimals could be quoted. For writing any numeral in the form of expansion we first have to jot down the face value and multiply it with the place value of all the numeric digits that are joined together by placing a sign of addition between them.
We will be doing the same to write decimal values in expanded type. For instance, let’s take the digit 24.578 and write it in expanded format. So, with the help of the table below let’s understand this, firstly writing all the figures on the chart of place value
Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
2 | 4 | . | 5 | 7 | 8 |
It can be observed that the place values are marked with the values of the face positioned along with each one of the numeric digits 24.578.
So, the 24.578 can be quoted in expanded form in the given order:
24.578 = 2 x 10 + 4 x 1 + 5 x 1/10 + 7 x 1/100 + 8 x 1/1000
24.578 = 20 + 4 + 0.5 + 0.07 + 0.008
Conclusion
It is simple to understand the connection between fractions and decimals as well as whole numbers. Through the various types of decimals, we can frame a picture of the nature of the decimals and the concept of place value. By constructing the place value chart, we can quickly know the position of the numbers as per their value of tenths, hundredths, or thousandths.
Also, by this, we got to know how to write a digit in decimal into its expanded format by adding the digits positioned at different place values and as well as the way of converting fractions to decimals.
