Decimal number is a number with a dot known as decimal point.
Decimal Number
Definition
A decimal number is a number having a whole number part and a fractional part separated by a decimal point.
Decimal Number Parts
We understand a decimal number elaborately by understanding each digit according to their place value.
Suppose we have a larger decimal number such as 724.365.
Thus joining the whole number and fractional part, we get the complete decimal number as shown below.
Decimal
Writing Decimals
In Expanded Form
We read a decimal number by its expanded form based on the place value of each digit in it. The fractional part in a decimal number represents the values according to the decimal place value chart.
We read a decimal number by the place values of all the digits in it.
For example, in the decimal number 6234.7815, in the whole number part, 6 is at the 1000s. In the fractional part, 5 is at the 10,000ths place.
Expanded Form with Decimals
That means 6 represents 6000, and 5 represents 0.0005
In Words
We can write the above number
For example, the number, 24.7 means ‘twenty-four and seven-tenths’.
Decimals in Words
If the number is 10 times smaller, the point shifts towards left. And, if the number is 10 times larger, the point shifts towards right.
Suppose 24.7 gets 10x smaller, it means it has to be divided by 10.
So, 24.7/10 = 2.47
The decimal point shifts to the left of 4 here.
If 2.47 gets 10x larger, means it has to be multiplied by 10.
So, 24.7 × 10 = 24.7
The decimal point shifts to the right of 4 here.
Write ‘fifty-five and three-tenths’ in decimal form.
Solution:
As we know, Three-tenths is 3/10 = 0.3 And fifty-five is the whole number. ∴ 55 + 0.3 = 55.3 So, fifty-five and three-tenths = 55.3
Write ‘sixty-eight and thirty-seven-hundredths in decimal form.
Solution:
As we know, Thirty-seven-hundredths is 37/100 = 0.37 And sixty-eight is the whole number. ∴ 68 + 0.37 = 68.37 So, sixty-eight and thirty-seven-hundredths = 68.37
Types of Decimals
Decimals are categorized based on the types of digits occurring after the decimal point.
1. Terminating Decimals
The digits after the decimal point do not reoccur in such decimals. The number ends after a finite number of decimal places. Example: 737.534, 65.2, etc.
2. Non-terminating Decimals
The digits are infinite after the decimal point in such decimals.
Example, 737.537269541…, 34.123123123…… etc. We can be further divide non-terminating decimals into 2 parts:
Recurring Decimal numbers: In such decimals, digits repeat after a fixed interval. Example: 5.232323…., 34.123123123… etc.
Non-recurring Decimal numbers: In such decimals, digits never repeat after a fixed interval. Example: 737.537269541………, 1.41421356237309504……… and so on.
