Recurring Decimal-Converting a Pure Recurring Decimal Into Vulgar Fraction

A fractional value whose denominator represents a numerical value with a power of 10 is called a decimal fraction. In mathematics sometimes it has been found that few decimals numbers do not have fixed numerical digits after decimals. Hence it is necessary to “convert a pure recurring decimal into a fraction” to evaluate some of the mathematical equations.

Basically, a decimal can be expressed when a numeric value includes a point of decimal to represent a whole figure along the fraction of the numbers. Arithmetically, figures can be categorized into numerous types of natural number, real number, rational number, and whole number. In this article, the major focus is given on decimal numbers. A decimal fraction is a fractional value whose denominator has a power of 10, for instance, 2/10, 8/10, 9/100 are some of the decimal fractions. In this article, the main priority is given to how to “convert a pure recurring decimal into a fraction”.

Recurring Decimal 

Repeating decimal is often known as a recurring decimal. It is a type of decimal value that consists of repeating numeric digits after a fixed interval followed by the point of the decimal. For instance, 56.27427427.., 69.464646…, are some of the recurring decimal numbers. Decimal values can be classified into numerous categories depending upon the types of numeric digits occurring after the point of decimals. It depends upon whether the numeric digits are repetitive, non-repetitive, ending, or never-ending.

Representation of recurring decimal

A decimal value in which a sequence of numeric digits or a definite digit repeats itself to the right of the point of decimal is termed as repeating or recurring decimal. It represents the decimal expression of numeric values whose digits are periodic which means its digits are repeating themselves at regular intervals and the infinitely recurring part is not equivalent to zero.

A repeating decimal is often known as a non-terminating numeric decimal that is a sequence of numeric digits or definite digits repeating itself continuously.

• Commonly, bars are utilized over the recurring numeric digits in the repeating decimals, for instance, 0.44444…= 0.4  [ (x̄)  represent = 4 ]
• Dot notation is commonly used to represent a repeating decimal. A dot over a particular numeric digit or digits represents which number is repeating itself, for instance, 0.5˙8 is equivalent to 0.588888 and 0.˙9˙8 is equivalent to 0.989898

Decimal numbers are basically of two types. They are as follows:

• “Terminating decimals”

• “Non-Terminating decimals”

• “Non-terminating repeating recurring decimal”

• “Non-terminating non-recurring decimals”

Terminating Decimal number

When the question is “how to convert a pure recurring decimal into a fraction”, one has to determine whether the number is a terminating or non-terminating decimal. A decimal numerical value that has definite numeric digits after the point of the decimal is called a terminating decimal number. The decimal position of the digits is finite. In fact, these decimal values are also known as actual decimal numbers.

Its decimal fraction can be easily expressed in the form of a/b where b is not equivalent to zero or it can be said that decimal numbers can be represented as rational numbers.

For example, 0.3, 9.527, 82.25 are some examples of terminating decimal numbers.

• 0.3 can be written as 3/10 where a = 3 and b = 10 and the position of the decimal is 1.
• 82.25 can be written as 8225/100 where a = 8225 and b = 100 and the position of decimal is 2.
• 9.527 can be written as 9527/1000 where a = 9527 and b = 1000 and the position of decimal is 3.

The decimal numbers which are Non-Terminating

A decimal value that has an unlimited number of numeric digits after the point of the decimal is called a non-terminating decimal number, for instance, 4.43333, 0.33333, and 5.6421846 are some basic examples of non-terminating decimal values.

Non-terminating decimal values can be classified into 2 types 

• Recurring decimals number
• Non-recurring decimal number

Conclusion

Throughout this article, recurring values, recurring numbers, kinds of recurring numbers, and the conversion of decimal systems into fractions are all explored. Recurring decimals are values that are consistently reproduced after the decimal point and are referred to as recurring numbers. Non-integer numbers are typically represented using decimal numbers, which are the industry standard. A number system can be stated as a fraction of another decimal number. Decimal numbers are numbers where a decimal point distinguishes between the whole number portion and the fractional portion of a number. Decimals can be used to represent both rational and irrational numerals in a mathematical context. The recurring decimal number can be easily expressed in the form of a mathematical expression to evaluate several equations. After being converted into decimal numbers, some real numbers produce recurring decimals, whereas all irrational values produce recurring decimals after being converted into decimal form, but only some rational numbers do so. Aside from that, a considerable number of solved instances have been provided to show each idea in detail in this article.