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.

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.

Decimal expansion of a rational number is terminating

Real numbers are merely the mixture of rational and irrational numerals, in the numeral system. In known, all the arithmetic functions can be achieved on these numerals and they can be expressed in the number line, also. The digits that when represented in decimal format are expressible as non-terminating and non-repeating decimals are understood as irrational numbers. So it is an irrational number. Then, x is a terminating decimal only when q is of the form 2r x 5s for some non-negative integers r and s. Since we understand that by theorem, if a is a prime numeral and if a ranges p 2 , then a divides p, where a is a positive integer. Equation 1 offers 3 as a factor of p and Equation 2 indicates that 3 is a factor of q. This is a paradox to our belief that p and q are co-peaks. Thus, the root of 3 is irrational. Thus, p is a common factor of r and s. But, this contradicts the fact that r and s have no common factor other than 1. Hence, p is irrational. This is a contradiction. Any rational numeral that is, a fraction in the lower times can be reported as either a terminating decimal or a repeating decimal.

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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.

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.

Decimal expansion of a rational number is terminating

Our terminating decimal calculator will teach you how to find the decimal representation of a number, detect the possible presence of repeating decimals , and much more. Keep reading to find out:. Additionally, we have prepared several examples of all the math explained in the text. We promise it will be interesting and surprisingly easy! What are you waiting for?

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Year 1 Maths Worksheets. The quotient thus obtained is the required decimal expansion. Contribute to the GeeksforGeeks community and help create better learning resources for all. Terminating Decimal Examples 4. The decimal expansion of the rational number terminates when the remainder becomes zero. Privacy Policy. Decimal numbers come in two varieties: repeating and non-repeating for the terminating and non-terminating numbers, respectively. Learn Terminating Decimal with tutors mapped to your child's learning needs. Irrational number. This is how we can find terminating decimals without division. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. Two types of decimal numbers may result from this process. Learn Practice Download.

Rational numbers can be represented as decimals.

For example, Saudi Arabia. We use cookies to ensure you have the best browsing experience on our website. One example of terminating decimal is 0. Terminating Decimal Numbers. Non-Terminating Decimal Numbers. Work Experiences. About Us. These numbers are called non-terminating decimals because the digits after the decimal point do not terminate. Natural number. But, this contradicts the fact that r and s have no common factor other than 1. Year 4 Maths Worksheets. Contribute your expertise and make a difference in the GeeksforGeeks portal. Find the right teacher.