Is 0.121212 rational

Answer 1

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).