Pure-recurring decimals can be defined as the decimals in which all the digits are repeated after the decimal point. The repeated decimals fractions are represented with a line.
Pure recurring decimals are decimals in which all the digits are repeated. An example of a pure recurring decimal can be \(0.\overline{48}\).
Conversion of Pure Recurring Decimal:
The steps are required to convert the pure recurring decimal into the vulgar fractions.
- At first, the bar needs to be removed from the top of the decimal fraction by putting it equal “n” variable.
- The repeating digits need to be written at least twice.
- Finding the number of digits having bars on its heads.
- Therefore, it must be noted that the conversion of pure recurring decimals can be determined by multiplying 10, 100, 1000 and so on.
- 10 need to be multiplied on the pure recurring decimal if the repeating decimal has 1 place of repetition.
- 100 need to be multiplied if the pure recurring decimal has 2 places of repetition.
- 1000 or more need to be multiplied if the pure recurring decimal has 3 or more places of repetition.
- The number needs to be subtracted which is obtained from the first step from the second step
- Both sides of the equation are divided with the coefficient of “n”.
The number of zeroes increases depending on the places of repetition in the pure recurring fractions. At last, the vulgar fraction is obtained from the pure recurring decimal, which is in its lowest form.
