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Decimal and It's Types

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Last updated date: 21st May 2024
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What is a Decimal?

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


Types of Decimal Numbers

There are many different types of Decimal Numbers as follows:


1. Terminating Decimal Numbers

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.


2. Non-Terminating Decimal Numbers

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.


3. 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.


4. Non-Recurring Decimal Numbers

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.


What is the Importance of Decimal Worksheets?

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.


Things to Keep In Mind

  • Decimal represents the integer Numbers as well as non-integer Numbers.

  • Decimal contains the 4 types of Decimals that are terminating Decimal Numbers, non-terminating Decimal Numbers, recurring Decimal Numbers, and non-recurring Decimal Numbers.

  • The types of the Decimal are all different so the students should clear their concepts regarding it.

  • Maths is all about playing with Numbers and some students might have an idea that Maths is tough but they don't understand that by practicing and understanding the topic they can actually ace in this subject.

  • It is okay if any student gets any answers wrong while solving the problems. It's normal to make mistakes by doing so they will get to know how to solve the answers.

  • Students are always recommended to practice every problem present in the book. Even the solved examples too because this will make them practice the problems more and they can have a clear idea how to solve the problem.

  • Students should be attentive in class because the teachers might cover everything which is needed in this topic. Those concepts are to be understood first so that they can know how the problems can be solved.

  • If they have problems understanding in classes they can study after they return from their schools. Students should first try to understand on their own if they are not successful then they can have a guide in order to have the concepts cleared.

  • Maths is all about practice and understanding how the problems are to be solved. So the students need to practice many times to make the concepts clear.

  • The formulas in Maths are the most important things which are to be remembered because they are required while solving the problems.

  • Formulas are important because to solve the problems they need to apply the formula and find the correct answers. Students need to solve the problems step-wise because while solving them step-wise there are more chances to get the problems solved.

  • In examination, they need to solve the problems step-wise because marks are given according to the step solved in the solutions.

  • Always maintain a copy and mention all types of formulas in Maths. This will help the students to have ideas of the formulas. So that they can remember and apply the formula when they need to solve the problems.

  • Every problem does not apply the same formula so students need to understand the questions and understand and apply the needed formula to it so that they can solve it in the right way.

  • Students tend to lose hope and patience when they are not able to solve the problems, this discourages them. Students need to have patience in Maths because there are more chances of getting the wrong answers while solving a problem. When they face something like this they are recommended to hire a tutor specifically for this subject and make time to solve more and more problems in order to have the practice of solving it.

  • Hiring tutors can help the students to guide the directions to solve the problems easily. Some tutors even have some tricks which can help the students to solve the problems easily.

  • Practice makes perfect in everything and practicing in Maths always makes perfect to solve the problems and it even helps the students to solve the problems at a fast pace.

  • In Maths, solving problems in a short time is challenging so they need to have practice in solving them. This will help in examinations so that they can get time to revise the answers.

  • Students can opt for online classes or tutoring in Vedantu. It offers the best services for the students, it has the best tutors for this subject who can solve the doubts which the students have.

  • Homework can be given to the tutors which will make the students have practice on how to solve the problems in an easier way and in the minimum time.

  • They can always have the solutions handy to check whether the method and the steps they used are correct while solving the problems.

  • The solution books can be downloaded from Vedantu's website in PDF form in mobile apps or even on the laptop. The PDF will help them to refer while solving the problems when they are needed. The solutions are given stepwise so that the students will have the knowledge of how to solve the problems.

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FAQs on Decimal and It's Types

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

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.

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 represent 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.