Give two rational numbers lying between 0.1911191119111119 … and 0.21211211121111 … .

We know, The numbers which cannot be expressed in the form of p q , where p and q are integers and q ≠ 0 are called irrational numbers. A number is said to be rational only if its decimal representation is repeated or terminating. Irrational numbers are non – terminating and non – recurring decimals. As we all know between these two irrational numbers there are infinitely many numbers possible some are rational numbers and some are irrational numbers. So, 0 . 192 and 0 . 193 is greater than 0 . 19111911191111119 . . . . . and less than 0 . 21211211121111 . . . . . Therefore, rational numbers 0 . 192 and 0 . 193 are lying between given irrational numbers.

Give two rational numbers lying between 0.1911191119111119 … and 0.21211211121111 … .

We know, The numbers which cannot be expressed in the form of p q , where p and q are integers and q ≠ 0 are called irrational numbers. A number is said to be rational only if its decimal representation is repeated or terminating. Irrational numbers are non – terminating and non – recurring decimals. As we all know between these two irrational numbers there are infinitely many numbers possible some are rational numbers and some are irrational numbers. So, 0 . 192 and 0 . 193 is greater than 0 . 19111911191111119 . . . . . and less than 0 . 21211211121111 . . . . . Therefore, rational numbers 0 . 192 and 0 . 193 are lying between given irrational numbers.

Find two irrational number between 0 . 30 ¯ and 0 . 31 ¯

We know, Irrational numbers are non-terminating and non-recurring decimals. 0 . 30 ¯ = 0 . 303030 . . . . . . . 0 . 31 ¯ = 0 . 313131 . . . . . . . The first three digits of the numbers are 0 . 303 and 0 . 313 , we can introduce two rational numbers between 0 . 303 and 0 . 313 , these are 0 . 304 and 0 . 305 . Now convert these three rational numbers into irrational numbers by writing 0 , 100 , 1000 and few dots after that. Therefore, 0.30404004000 ………. and 0.30505005000 ……….. are the two irrational numbers.

Find two irrational number between 0.5 2 - and 0 . 52 -

We know, Irrational numbers are non-terminating and non-recurring decimals. 0 . 5 2 ¯ = 0 . 522222 . . . . . . . 0 . 52 ¯ = 0 . 525252 . . . . . . . The first three digits of the numbers are 0 . 522 and 0 . 525 , we can introduce two rational numbers between 0 . 522 and 0 . 525 , these are 0 . 523 and 0 . 524 . Now convert these three rational numbers into irrational numbers by writing 0 , 100 , 1000 and few dots after that. Therefore, 0.523010010001 ……….. and 0.524010010001 ……….. are the two-irrational numbers.