Decide whether the real numbers are rational or not. If they are rational ,then write its p/q form.What can you say about the prime factors of q?

R: set of real numbers  Q: set of rational numbers  Therefore, R – Q is a set of irrational numbers.

Solution: No. Justification: Consider the positive integer 3q + 1, where q is a natural number. => (3q + 1)2 = 9q2 + 6q + 1 = 3(3q2 + 2q) + 1 = 3m + 1,...

The product of a non zero rational and an irrational number is always irrational 

Solution: i. Since the given number has a terminating decimal expansion, it is a rational number of the form p/q and q is of the form 2m x 5n. The prime factors of...

Solution: 327.7081 = 3277081/10000 = 3277081 / 24 x 54 = p/q Here, q is of the form 2m × 5n, where m and n are natural numbers. The prime factors of p and q will...

Inner transition metals are those elements in which the last electron enters the f-orbital. The elements in which the 4f and the 5f orbitals are progressively filled are called f-block...

(i) 0 (ii) 1 and -1 (iii) 0

As 1.7351 is a terminating decimal number, so q must be of the form 2m 5m where m ,n are natural numbers.

R: set of real numbers Q: set of rational numbers Therefore, R – Q is a set of irrational numbers.

Inner transition elements have atomic numbers from 58 to 71 and 90 to 103. Hence, the atomic numbers 59, 95 and 102 are the atomic numbers of the inner transition...