Decimal expansion of a rational number is terminating

Let's first define rational numbers before discussing how they are represented when expanded to decimal form.

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. It is a decimal that has an end-digit. A decimal is a number that consists of a whole number and a fractional part. There are two types of decimals categorized on the basis of the number of digits after the decimal point. If you have two chocolates and you ate half of one of the chocolates, then you are left with 1. This is a terminating decimal since there is only one digit after the decimal point.

Decimal expansion of a rational number is terminating

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. But there are also some rational numbers where the division process does not get terminated as shown in the above example. Depending on the remainder we get and the length of the quotient, we can classify the decimal expansion into two types. A terminating decimal expansion of a rational number means that while using the long division method we will get a fixed number of digits in the quotient.

Correct answer is: 8.

The terminating decimal expansion means that the decimal representation or expansion terminates after a certain number of digits. About Us. Already booked a tutor? Learn Ncert All Solutions with tutors mapped to your child's learning needs. Learn Practice Download. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions. In each case, decide whether they are rational or not.

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. Also the terminating decimals such as 0. For e. Similarly, the numbers 0.

Decimal expansion of a rational number is terminating

In Mathematics, a real number is a combination of rational numbers and irrational numbers. The rational and irrational numbers can be expressed in their decimal form. The real numbers can be represented using the number line.

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Year 4 Maths Worksheets. For example, Add Decimals. Hence the division never gets terminated and the quotient goes upto infinity. Perimeter of rhombus with diagonals. Please go through our recently updated Improvement Guidelines before submitting any improvements. Skip to content. It is a decimal that has an end-digit. The decimal 1. The table given below shows examples which will help you in identifying terminating decimals better.

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.

Learn Ncert All Solutions with tutors mapped to your child's learning needs. No, pi is not a terminating decimal as the value of pi is 3. Natural number. The rational number whose denominator has no factors other than 2 and 5 gives a terminating decimal number. Explore math program. Real numbers are merely the mixture of rational and irrational numerals, in the numeral system. Our Team. None of these. Important Links. Decimal numbers that are stated as rational numbers may be repeating decimals that terminate or do not.