(i) 7.478478….
We know that 7.478478…. is a non-terminating recurring decimal, which can be converted into p/q form.
While, converting 7.478478…. into p/q form, we get
x = 7.478478.... ...(a)
1000x = 7478.478478.... ....(b)
While, subtracting (a) from (b), we get
We know that 999x = 7471 can also be written as x= 7471/999.
Therefore, we conclude that 7.478478…. is a rational number.
(ii) 1.101001000100001....
We can observe that the number 1.101001000100001.... is a non terminating non recurring decimal.
We know that non terminating and non recurring decimals cannot be converted into p/q form.
Therefore, we conclude that 1.101001000100001.... is an irrational number.
