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In mathematics, Decimals are used to represent fractional value and the whole number together. In mathematics sometimes it has been found that few decimals numbers do not have fixed numerical digits after the decimals. Hence it is necessary to convert mixed recurring decimals into fractions to evaluate some of the mathematical equations.

Generally, a decimal value is represented when a numeric value includes a point of decimal to represent a whole figure along with the figure of the number. Basically, the fractional value is separated from the whole numerical values by using “.”, this dot represents the point of the decimal. In mathematics, numbers are classified into various types such as natural numbers, real numbers, rational numbers, and whole numbers. Decimal numbers are one of the types of figures that can be found in mathematics. Decimal expansion can be represented in two types, terminating and non-terminating. In this article, the main focus is on mixed recurring decimals which are a part of non-terminating decimal.

Types of Decimals

Decimals can be expanded into two categories:

  • Terminating 
  • Non-terminating

Non-terminating decimals can be further categorized into two parts: Repeating or recurring decimal numbers and Non-repeating decimal numbers.

 Recurring decimal can be further classified into two parts:

  • Pure recurring decimal number
  • Mixed recurring decimal number

Terminating decimal

When the question is about mixed recurring decimal one has to understand the broader concept of the decimal. A decimal numerical value that has definite numeric digits after a point of the decimal is called a terminating decimal number. The decimal position of the digits is finite. These decimal values are also known as exact decimal numbers. If decimal fraction can be easily expressed in the form of p/q where q is not equivalent to zero or it can be said that decimal numbers can be represented as rational numbers.

For instance, 0.4, 8.546, 75.45 are some of the examples of terminating decimals numbers.

  • 0.4 can be written as 4/10 where p = 4 and q = 10 and the position of decimal is 1.
  • 75.45 can be written as 7545/100 where p = 7545 and q = 100 and the position of decimal is 2
  • 8.546 can be written as 8546/1000 where p = 8546 and q = 1000 and the position of decimal is 3.

Non-terminating decimal

A decimal value that has an unlimited number of numeric digits after a point of the decimal is called a non-terminating decimal number, for instance, 6.25555, 0.41111, and 8.48412 are some of the common decimal figures of non-terminating decimal values. Non-terminating decimals are of two types: recurring decimal and non-recurring decimal. 

Recurring decimal number 

When the question is what is mixed recurring decimal on has to understand what is a recurring decimal. Repeating decimal also known as a recurring decimal is a set of numerical values which are repeated again and again in a decimal fractional value, for instance, ⅓ is equivalent to 0.333, and 1/7 is equivalent to 0.142857142857 where “142857” is repeated again and again. Recurring decimal expansion can be classified into two types:

  • Pure recurring decimal
  • Mixed recurring decimal

Significance of mixed recurring decimal

In mathematics, some of the decimal fractional values have some of the digits which are repeating and some of the digits are not repeating, these decimal fractional values are known as mixed recurring decimals.  It can also be said that mixed recurring decimal contains at least one numerical digit which is not repeating after the point of decimal and some numerical digits are repeating. Some of the basic examples are represented as follow:

  • 5/18 where 5 can easily get divided by 18 and the quotient obtained is 0.2777… which shows the digit 7 is repeating continuously.

Identification of mixed recurring decimal

Identification of mixed recurring decimal is quite easy and it can be followed through these steps:

  •  The first step is a division of numerators with the given denominator presented in the form of a fraction.
  • The next step is to check if at least one numerical digit behind the point of decimal is repetitive and flowing numerical digits are repeating themselves or not.
  • If the following conditions are followed and matched then the fractional value is a mixed recurring decimal.

For example, to identify 19/6 in a form of decimal and if it mixed recurring decimal, it can be evaluated following ways: 

  • The first step is to divide 19 by the numeric value 6
  • After the division, the following result represents 3.16666…..
  • Since the result show, only one numeric value 6 repeats itself again and again. Hence 19/6 can be recognized as a mixed recurring decimal.

Conclusion

In conclusion, through the following article, it can be concluded that terminating numbers, non-terminating numbers, repeating decimal numbers, and non-repeating numbers are all explored. It has been found that recurring decimal can be further classified into two parts, firstly pure recurring decimal and secondly, mixed recurring decimal. Recurring decimals are the values that are consistently repeated after the point of the decimal. A decimal number is a number where the point of decimal segregates the fr5actional portion from the whole value. The recurring decimal number can be easily expressed in the form of mathematical expressions to evaluate several equations.