Is 0.151515 a rational or an irrational?

Answer 1

As given as ' 0.151515 . it is a terminating decimal and can be converted to a fraction/ratio

Hence

0.151515/ 1.000000 = 0151515/1000000 = 151515/1000000 = 30303/200000 is the fraction.

However, if you mean 0.151515 recurring to infinity, it is also rational.

It should be written as ' 0.151515.... ' Note the three or more dots after the last digit.

To convert to a ratio/quotient/fraction

Let

P = 0.151515....

100P = 15.151515....

Subtract

99P = 15 Note the recurring decimals subtract to zero.

P - 15/99

Reduce by '3'

P = 5/33 The ratio/fraction.

NB When reading decimal numbers. If it recurs to infinity, AND the decimal digits are in a regular order , as in this case at '151515' , then it is NOT irrational.

e.g.

0.123123123.... Is rational

or

0.1234512345..... is rational

etc.,

because the decimal digits are in a regular order, and can be converted to a ratio/fraction/quotient.

Answer 2

0.151515(not repeating) is rational. Rational numbers are numbers that can be written as a fraction. Irrational Numbers cannot be expressed as a fraction.

Answer 3

Irrational