Decimal expansion of a rational number is terminating

A terminating decimal is a decimal in which the digits after the decimal point terminate. This means that the digits after the decimal are finite in number.

Decimal expansion of rational numbers means when we represent a rational number given in the form of a fraction in the form of a decimal. We use the long division method for this process of conversion. In this math article we will study the decimal expansion of rational numbers. We use the long division method for this process. When we perform the long division method, the quotient obtained after division is the required equivalent value of our rational number in the decimal form. Here as we are not getting the remainder 0 so we terminate the division and consider the quotient got so far. We see that for some rational numbers we get a certain fixed value of the decimal equivalent.

Decimal expansion of a rational number is terminating

Terminating decimals are the numbers that have a fixed or a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole, just like fractions. In this lesson, we will focus on the type of decimal numbers, that is, terminating decimal numbers. The word 'terminate' means to bring to an end. In terms of decimal, it is a number that ends. In this article, we will learn what are terminating decimals and the ways to recognize these numbers. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. Decimals are used to express the whole number and fraction together that is separated from each other by inserting a ". For example, There are different categories of decimals depending on what type of digits occur after the decimal point, they are:. A number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. A rational number has either a terminating decimal expansion or a non-terminating recurring decimal expansion.

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Let's first define rational numbers before discussing how they are represented when expanded to decimal form. Decimals are what is produced when these numbers are further simplified. The decimal expansion of a rational number is obtained by dividing the numerator by the denominator of the rational number. Decimal Expansion. By dividing a rational number's numerator by its denominator, one can get the decimal expansion of a rational number.

Terminating decimals are the numbers that have a fixed or a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole, just like fractions. In this lesson, we will focus on the type of decimal numbers, that is, terminating decimal numbers. The word 'terminate' means to bring to an end. In terms of decimal, it is a number that ends. In this article, we will learn what are terminating decimals and the ways to recognize these numbers. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. Decimals are used to express the whole number and fraction together that is separated from each other by inserting a ".

Decimal expansion of a rational number is terminating

Before going into a representation of the decimal expansion of rational numbers, let us understand what rational numbers are. So when these numbers have been simplified further, they result in decimals. Let us learn how to expand such decimals here. Examples: 6 , The real numbers which are recurring or terminating in nature are generally rational numbers. For example, consider the number It can be seen that the decimal part.

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Can every rational number be represented as a decimal number? Terminating Decimal Numbers. Decimal expansion of rational numbers means when we represent a rational number given in the form of a fraction in the form of a decimal. Year 6 Maths Worksheets. The terminating decimal expansion means that the decimal representation or expansion terminates after a certain number of digits. Depending on the remainder we get and the length of the quotient, we can classify the decimal expansion into two types. Thus we consider the required answer to be upto where the recurring starts. Real numbers are merely the mixture of rational and irrational numerals, in the numeral system. Maths Program. So, it is a terminating decimal. Let us take some examples of rational numbers and find their decimal expansion.

Rational numbers can be represented as decimals. The different types of rational numbers are Integers like -1, 0, 5, etc. The decimal representation of a rational number is converting a rational number into a decimal number that has the same mathematical value as the rational number.

Complete Tutorials. Decimals are used to express the whole number and fraction together that is separated from each other by inserting a ". Online Tutors. A rational number has either a terminating decimal expansion or a non-terminating recurring decimal expansion. In other words, these numbers end after a fixed number of digits after the decimal point. Help us improve. The quotient 0. More Articles for Maths. Maximize your earnings for your published articles in Dev Scripter ! Our Journey. Example 2: Look at the following pie charts. Year 11 Maths Worksheets.