Recurring Decimals

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.

Decimal to Fraction Calculator

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