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Mathematics is all about playing with numbers. The numbers are classified into various types of numbers such as real numbers, natural numbers, whole numbers, and rational numbers, and so on. Decimal numbers are among all these numbers. Decimals are the standard form of representing integer numbers as well as non-integer numbers.

In the topic of Algebra, decimals are one of the types of numbers. The decimal number has a whole number and also a fractional part separated by a decimal point. The dot that is presented between the whole number and the fractional part is known as the decimal part. For Example, 45.7 is a decimal number where 45 is the whole number part and 7 is the fractional part. The “.” Is the decimal point of the decimal number 45.7

There are many different types of decimal numbers as follows:

The terminating decimal numbers have a finite number of digits just after the decimal point. Such a type of decimal number is known as an exact decimal number. The number of digits after the decimal point of the terminating decimal numbers is countable.

For Example-

98.678

34.9807

-5.8764

All these decimal numbers are examples of the terminating decimal numbers or the exact decimal numbers. The reason behind this is the numbers of digits after the decimal point is finite. These decimal numbers can be written in the form of p/q and therefore they are rational numbers. The rational numbers are those numbers that can be written in the p/q form where the value of q is not equal to zero.

The non-terminating decimal numbers are the numbers where the digits after the decimal point of non-terminating decimals repeat endlessly.

In other words, one can also say that the decimal numbers have an infinite number of digits after the decimal point. The non-terminating decimals are further divided into recurring as well as non-recurring decimal numbers.

The recurring decimal numbers are those numbers that have an infinite number of digits after the decimal point. However, these digits are repeated at regular intervals.

For Example-

4.787878…

9.505050…

These are the examples of recurring decimal numbers as the number of digits after the decimal point is repeated after regular intervals or follow a specific order.

These numbers can also be written by simply putting a bar sign over the number that is repeated after the decimal point.

These numbers can also be written in fractional form and therefore they are also rational numbers.

The recurring decimal numbers can be pure periodic or ultimately periodic.

The non-recurring decimal numbers are the non-terminating as well as the non-repeating decimal numbers. The non-recurring decimal numbers have an infinite number of digits at their decimal places and also their decimal place digits do not follow a specific order.

For Example-

56.78965…

789009.97658…

45.7789…

All the above numbers are examples of non-recurring decimal numbers where we cannot put a bar sign over the decimal numbers because the digits after the decimal point follow no repetitive order.

These decimal numbers cannot be written in the p/q form and therefore they are irrational numbers.

A decimal number is any number that forms the base ten number frameworks. In the worksheets, there will be a focus on the numbers that have at least one digit to the director of the point.

The worksheets will help the students in better-understanding of decimal numbers. The decimal point helps in isolating the one spot from the tenths spot in the decimal number. While isolating dollars from pennies, the concept of decimal will be useful.

Decimals are used in our everyday life, when we are dealing with money, length, weight, etc., we always use the decimal system. The decimal system is used in situations where one needs more precision than the whole number can provide.

For example, when one goes to the market for grocery items, the weight is calculated using the decimal system in the weighing machine. To know the exact weight of the item's decimal system helps in getting to know the exact weight than a whole number.

The decimal system is also used in other situations. While converting paisa into rupee, the decimal system is used to get the exact number. While measuring the length of an item, it is always not necessary that the length of an object will be a whole number. The length can also be in decimal.

FAQ (Frequently Asked Questions)

1. What is Meant By Decimals? What are Pure Periodic and Ultimately Periodic Decimal Numbers?

Ans: Decimals are numbers that consist of two parts. One part is a whole number and the other part is the fractional part which is separated by a decimal point.

For Example-

67.4 is a decimal number where 67 is the whole number and 4 is the fractional part which is separated by a decimal point.

Pure periodic decimals are those decimal numbers where the decimal part is repeated infinite times.

For Example-

789.666…., 34.6666…, 7.999…

Ultimately periodic decimal numbers are numbers in which a periodic part is followed by a non-periodic part.

For Example-

567.899.., 45.9888…

2. Write about the Arithmetic Operation on Decimals.

Ans:

**Addition**

When a decimal number is added then line up the decimal points of the given number and add the numbers. If a decimal point is not visible then the decimal is behind the number.

**Subtraction**

While subtracting decimal numbers, line up the decimal point of given numbers and then subtract the values. To carry out the arithmetic operation use a place holding zeros' for reference.

**Multiplication**

One needs to multiply the given numbers like the integers as if the decimal point does not exist. After finding the products count up the numbers present after the decimal point of both the numbers which represents the numbers that are required after the decimal point.

**Division**

Perform the division operation like the integer division after moving the decimal point in the number such that the number becomes a whole number.