**Number System Important Questions For Class 9 (Chapter 1)**

Q.1: Find five rational numbers between 1 and 2. [Answer: 7/6, 8/6, 9/6, 10/6, 11/6]

Q.2: Find five rational numbers between 3/5 and 4/5. [Answer: 19/30, 20/30, 21/30, 22/30, 23/30]

Q.3: Locate √3 on the number line.

Q.4: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Q.5: Find the decimal expansions of 10/3, 7/8 and 1/7.

Q.6: Show that 0.3333… = 0.3- can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Q.7: What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

Q.8: Find three different irrational numbers between the rational numbers 5/7 and 9/11. [Answer: 0.720720072000.., 0.730730073000…, 0.808008000…]

Q.9: Visualise 3.765 on the number line, using successive magnification

Q.10: Add 2√2+ 5√3 and √2 – 3√3. [Answer: 3√2 + 2√3]

Q.11: Simplify: (√3+√7) (√3-√7). [Answer: -40]

Q.12: Rationalise the denominator of 1/[7+3√3].

Q.13: Represent √(9.3) on the number line.

Q.14: Simplify:

(i)7^{2/3}.7^{1/5}

(ii)10^{1/2}/10^{1/4}