Decimals are a very important part of the number system. It is considered as the standard form of representing both integers and non-integers. Want to know the basic concept of decimal numbers? Through this article, you can learn all about decimals including the meaning, place value system, types, and properties of the decimals.
Decimals in mathematics are the set of numbers in which a decimal point separates the whole number from the fractional part. Decimal numbers consist of a point referred to as decimal point, which separates the whole number and fractional part. The numbers which are written to the left side of a decimal point are integers and the numbers written to the right side of the decimal point are referred to as decimal numbers.
For example, 40.78 is a decimal number. Here, the whole part is 40 and the fractional part is 78. The point (.) between 40 and 78 is the decimal point.
Place value system for the numbers written after the decimal point is completely different from the place value system for the numbers written before the decimal point. The digits written before the decimal point are multiplied with positive powers of ten in increasing order from right to left. In the case of numbers written after the decimal point, digits are multiplied with negative powers of ten in decreasing order from left to right.
The decimals are categorized based on the type of digits occurring after the decimal point. Let’s take a look at different types of decimals:
- Terminating decimals: Terminating decimals is the one in which the digits after the decimal point do not reoccur and end after a finite number of decimal places. For example, 423.67843, 67.2, 6.897, etc.
- Non-terminating decimals: Non-terminating decimals are the ones in which the digits after the decimal point reoccur and do not end after a finite number of decimal places. For example, 342.673295324696524.
The non-terminating decimals are categorized into two more parts:
- Recurring decimals: Recurring decimals are the ones in which digits after the decimal point repeat after a fixed interval. For example, 7843.265265265, 98.676767, etc.
- Non-recurring decimals: Non-recurring decimals are the ones in which digits after the decimal point never repeat after a fixed interval. For example, 345.6434789…., 97645.752394…, etc.
Here are some properties of decimal numbers under the operations of multiplication and division:
- When any two decimal numbers are multiplied in any order, then the product computed remains the same.
- When a whole number and a decimal number are multiplied in any order, then the product computed remains the same.
- When a decimal fraction is multiplied by 1 then the product computed is the same as the decimal fraction.
- When a decimal number is multiplied by zero then the product computed is also zero.
- When a decimal number is divided by one, then the quotient computed is equal to the decimal number.
- When the decimal number is divided by the same number then the quotient computed is equal to one.
- When zero is divided by any decimal number the quotient computed is equal to zero.
- It is not possible to divide the decimal number by zero, as the reciprocal of zero doesn’t exist.
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