Worksheet (IXth ) Q.1 Which of the following statements are true and false . (i) Every natural number is a whole number. (ii) Every whole number is an integer . (iii) Every whole number is a natural number. (iv) Every integer is a rational number. (v) Every whole number is a rational number. Q.2 Find five rational numbers between and . Q.3 Find six rational numbers between 2 and 3. Q.4 Write the following in decimal form and say what kind of decimal expansion each has: (i) (ii) (iii) (iv) Q.5 Classify the following as rational or irrational numbers: (i) √17 (ii) √169 (iii) √0.0144 (iv) √ √ . Q.6 Find an irrational number between Q.7 Express the following on the number line : (i) √5 (ii) √7 (iii) √9.37 (iv) √17 Q.8 Visualize 3.765 on the number line using successive magnification. Q.9 Rationalise the denominators of the following real numbers: (i) √ (ii) √ (iii) √ (iv) √ √ Q.10 Simplify : (i) (9) (ii) (25) (iii) (49) (iv) (v) X ÷ Q.11 Recall , is defined as the ratio of the circumference (say c ) of a circle to its diameter (say d ). This is π = . This seems to contradict the fact that π is irrational . How will you resolve this contradiction ?
Q.12 If x = √ and = p√7, find the value of the rational number p. Q.13 Simplify the following expression : (i) √ + √ (ii) √ √ + √ √ Q.14 Visualize the position of 5.665 on the number line , through successive magnification . Q.15 Write five integers immediately on the left‐hand side of integer – 1095.