Recurring decimals are decimal representations that repeat one or more digits forever after the comma. In recurring decimal notations, a dash is placed on repeating numbers to show that that number is recurred.
E.g; 0.333333… is expressed as $0,\overline{3}$ to show that the number 0.33333… rolls over the number 3.
$0,333\ldots =0,\overline{3}$
Similarly;
$1,242424\ldots =1,\overline{24}$
$4,455555\ldots =4,4\overline{5}$
$6,9787878\ldots =6,9\overline{78}$
Recurring decimal numbers can be written in rational number form with the following formula.
$\dfrac{Entire Number – Non-Transfer Part}{“9” up to the number of recurring decimals on the Right Side of the Comma and “0” up to the number of non-recurring decimals}$
Examples:
$0,\overline{6}=\dfrac{6-0}{9}=\dfrac{6}{9}$
$2,\overline{3}=\dfrac{23-2}{9}=\dfrac{21}{9}=\dfrac{7}{3}$
$1,2\overline{6}=\dfrac{126-12}{90}=\dfrac{114}{90}=\dfrac{19}{15}$
$3,\overline{41}=\dfrac{341-3}{99}=\dfrac{338}{99}$
You can find the fractional equivalents of decimals with the decimal fraction calculator below.