Non Repeating Decimal
Introduction to Non repeating decimal :
Introduction to Non repeating decimal :
Non repeating decimal is nothing but the number which is not repeated by a notation in decimal. Figuring the decimal numbers are mainly obtained from the fraction part. Moreover we refer the decimal notation for tenth, hundredthplaces. If the denominator is a power of ten such fractions are said to be decimal fractions. Let us we discuss about the non repeating decimal in brief.
Non Repeating Decimal:
In decimal, we have two types,
Repeating decimals: It is nothing but a decimal which repeats often like, 4.22222222222222
Non repeating decimals: Its nothing but the decimal value of the result is an non repeating values like, 5.8915763
Steps to perform the decimal operation is given below,
First perform the division operation for both numerator and the denominator.
The answer we obtained is either in the decimal form or in whole number.
When the result is in decimal notation then the notation is said to be a decimal notation is represent in the form of dot. Example: 55.2.
Example for Non Repeating Decimal:
Example for non repeating decimal 1: Convert '6/5' to a decimal notation
From the given question we came to know that, we have to divide 6 by using 5
Solution: Divide 6 by 5:
= 6 5
= 1.2
Here the steps shown above is the procedure to solve the division operation and the answer obtained is 1.2
Answer: '6/5' = 1.2
Example for non repeating decimal 2: Check whether the given 9/8 to a decimal notation
From the given question we came to know that, we have to divide 9 by using 8
Solution: Divide 9 by 8:
= 9 8
= 1.125
Here the steps shown above is the procedure to solve the division operation and the dot answer obtained is 1.125
Answer: '5/9' = 1.125
Example for non repeating decimal 4: Convert 5/79 to a decimal notation
From the given question we came to know that, we have to divide 5 by using 79
Solution: Divide 5 by 79:
= 5 79
= 0.0632911
Here the steps shown above is the procedure to solve the division operation and the answer obtained is 0.0632911
Answer: '4/80' = 0.0632911
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In arithmetic, repeating decimal is a way of representing a rational number. Thus, a decimal representation of a number is called a repeating decimal (or recurring decimal) if at some point it becomes periodic, that is, if there is some finite sequence of digits that is repeated indefinitely. For example, the decimal representation of 1/3 = 0.3333333 or 0.3 (spoken as "0.3 repeating", or "0.3 recurring") becomes periodic just after the decimal point, repeating the single-digit sequence "3" infinitely. A somewhat more complicated example is 3227/555 = 5.8144144144, where the decimal representation becomes periodic at the second digit after the decimal point, repeating the sequence of digits "144" indefinitely.
Rational numbers are numbers that can be expressed in the form a/b where a and b are integers and b is non-zero. This form is known as a common fraction. On the one hand, the decimal representation of a rational number is ultimately periodic, as explained below. On the other hand every real number which has an eventually periodic decimal expansion is a rational number. In other words the numbers with eventually repeating decimal expansions are exactly the rational numbers (i.e.: those that can be expressed as ratios).
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