For what value of n , 2 n × 5 n ends in 5 .

We have, 2 n × 5 n For checking the value n , so that given expression ends in 5 So, 2 n × 5 n = 2 × 5 n = 10 n If n = 0 , 10 n = 10 0 = 1 If n = 1 , 10 n = 10 1 = 10 If n = 2 , 10 n = 10 2 = 100 And so on. Thus, there is no value of n for which 2 n × 5 n ends in 5 .

Has the rational number 441 2 2 × 5 7 × 7 2 a terminating or a non-terminating decimal representation?

We have, 441 2 2 × 5 7 × 7 2 On simplifying the given number into its lowest term, we get 441 2 2 × 5 7 × 7 2 = 9 × 7 2 2 2 × 5 7 × 7 2 = 9 2 2 × 5 7 We see that the given rational number in its lowest form has its denominator of the form 2 m × 5 n . Therefore, the decimal expansion of the given rational number has a terminating decimal represantation.

Write whether 2 45 + 3 20 2 5 , on simplification, gives a rational or an irrational number.

We have a number 2 45 + 3 20 2 5 For checking the number is a rational or an irrational 2 45 + 3 20 2 5 = 2 3 × 3 × 5 + 3 2 × 2 × 5 2 5 = 2 × 3 5 + 3 × 2 5 2 5 = 6 5 + 6 5 2 5 = 12 5 2 5 = 6 We know, 6 = 6 1 , which is in the form of p q , q ≠ 0 . Therefore, on simplification, the given number gives a rational number.