Recurring decimals can be defined as the repeating decimals in which several digits or sequences of digits after the decimal point are repeated. The decimal representation depends upon the digits, whether they are terminating or repeating. The decimal numbers are categorized into three types. Terminating decimals where the decimals come to an end after certain digits. Secondly, there are recurring decimals in which a sequence of digits repeat itself an infinite number of times. For example, 1 / 3 is represented as 0.3333… Lastly, there are irrational decimals, these decimals also repeat their digit after the decimal point, but they are not into any sequence or pattern.
Decimals are the mathematical expression that denotes a combination of a whole number and a fractional number. It is represented by partitioning the numbers by a dot. The left side of the dot denotes the whole number whereas the right side of the dot denotes the fractional number. A whole number can be from 0 to infinity, however, the fraction number is always less than 1. The decimals are further categorized as terminating, the decimals that have a limited number of digits after the dot, for example, ½ will be represented as 0.5, and non-terminating decimals, the decimals that do not have any limit i.e., infinity, for example, ⅓ will be represented as 0.3333… which are non-terminating. The non-terminating decimals are further divided as recurring decimals, the decimals that repeat themselves in a pattern and non-recurring decimals that do not have any pattern or sequence but are extended till infinity, for example, the value of pi is extended till infinity but there is no sequence or pattern.
The recurring decimals meaning states that these are these decimals that are defined as repeating decimals. A decimal is known as a recurring decimal when the digits after the decimal point start repeating themselves in a sequence for an infinite number of times. An equation related to recurring decimals may become very complex to solve as the digits reach up to infinity. It is said that the recurring decimal took its birth during Ancient Egyptian time. However, the recurring decimal is used to represent various fractions as well as the square roots of several numbers in decimal form to ease out the calculations.
The recurring decimal is represented in a different way as per the adaptation of several countries. The most common representation of the recurring decimal is the Vinculum, i.e., a bar over the digit or the sequence of the digit.
If the fraction is 1/9, its recurring decimal will be 0.11111111, which can be represented as 0.1
Several other representations of the recurring decimal are:
Converting a recurring decimal into a fraction is quite easy. Questions related to the recurring decimals converting into fractions are quite basic in the mathematical quantitative aptitude exams. In order to convert a recurring decimal into a fraction, follow the given steps:
One of the recurring decimals examples that might help in practice:
Considering a recurring decimal 0.3333…
x= 0.444…
10x= 4.444…
10x-x=4.4444-0.4444…
9x= 4
X= 4/9
Therefore, the fraction for the recurring decimal is 4/9.
The recurring decimal numbers are the repeating decimals, which are composed of a digit or a pattern of digits that repeat themselves after the decimal point for infinity. The recurring decimal is categorized into three types, i.e., The Terminating decimal, The Recurring decimal, and the Irrational decimal. Bars, dots and even ellipses represent these decimals according to the easement. The recurring decimals help in simplifying various fractional numbers as well as the square root of digits to simplify the overall equation for easy calculation. To understand the recurring decimal better, it is required to have the basic knowledge of fraction and fractional numbers.
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