Is 0.121212 rational? - Answers

YES!!!! However, do you means 0.121212 as a terminating decimal or 0,121212,,,, as a recurring to infinity decimal? Note the three or more full stops, which mathemtically indicates a recurring decimal. As a terminatinf decimal 0.121212 / 1.000000 => 121212/1000000 Reduce by '2' 60606 / 500000 And again 30303 / 250000 the fraction/ratio As a Recurring to infinity decimal. Let P = 0.121212.... 100P = 12.121212.... Subtract 99P = 12 ( NB the recurring decimal subtract to zero). P = 12/99 Reduce by '3' P = 4/33 So in both forms of decimal it has been converted to a 'RATIO/fraction/quotient'. Hence it is a rational number. NB Irrational Numbers are those were the decimals go to infinity AND there is no regular order in the decimal digits. pi = 3.141592.... is the most well known irrational number. (Note the irregularity of the digits).