Page 1 NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 1 – Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form , where p and q are integers ? 0? and q Answer: Yes. Zero is a rational number as it can be represented as etc. Question 2: Find six rational numbers between 3 and 4. Answer: There are infinite rational numbers in between 3 an d 4. 3 and 4 can be represented as respectively. Therefore, rational numbers between 3 and 4 are Question 3: Page 2 NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 1 – Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form , where p and q are integers ? 0? and q Answer: Yes. Zero is a rational number as it can be represented as etc. Question 2: Find six rational numbers between 3 and 4. Answer: There are infinite rational numbers in between 3 an d 4. 3 and 4 can be represented as respectively. Therefore, rational numbers between 3 and 4 are Question 3: NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Find five rational numbers between Answer: There are infinite rational numbers between . Therefore, rational are Question 4: State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. Answer: (i) True; since the collection of whole numbers contains all natural numbers. (ii) False; as integers may be negative but whole numbers are positive. For example: -3 is an integer but not a whole number. (iii) False; as rational numbers may be fractional but whole numbers may not be. For example: is a rational number but not a whole number. numbers between . Page 3 NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 1 – Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form , where p and q are integers ? 0? and q Answer: Yes. Zero is a rational number as it can be represented as etc. Question 2: Find six rational numbers between 3 and 4. Answer: There are infinite rational numbers in between 3 an d 4. 3 and 4 can be represented as respectively. Therefore, rational numbers between 3 and 4 are Question 3: NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Find five rational numbers between Answer: There are infinite rational numbers between . Therefore, rational are Question 4: State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. Answer: (i) True; since the collection of whole numbers contains all natural numbers. (ii) False; as integers may be negative but whole numbers are positive. For example: -3 is an integer but not a whole number. (iii) False; as rational numbers may be fractional but whole numbers may not be. For example: is a rational number but not a whole number. numbers between . NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Exercise 1.2 Question 1: State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form , where m is a natural number. (iii) Every real number is an irrational number. Answer: (i) True; since the collection of real numbers is made up of rational and irrational numbers. (ii) False; as negative numbers cannot be expressed as the square root of any other number. (iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number. Question 2: 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. Answer: If numbers such as are considered, Page 4 NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 1 – Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form , where p and q are integers ? 0? and q Answer: Yes. Zero is a rational number as it can be represented as etc. Question 2: Find six rational numbers between 3 and 4. Answer: There are infinite rational numbers in between 3 an d 4. 3 and 4 can be represented as respectively. Therefore, rational numbers between 3 and 4 are Question 3: NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Find five rational numbers between Answer: There are infinite rational numbers between . Therefore, rational are Question 4: State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. Answer: (i) True; since the collection of whole numbers contains all natural numbers. (ii) False; as integers may be negative but whole numbers are positive. For example: -3 is an integer but not a whole number. (iii) False; as rational numbers may be fractional but whole numbers may not be. For example: is a rational number but not a whole number. numbers between . NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Exercise 1.2 Question 1: State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form , where m is a natural number. (iii) Every real number is an irrational number. Answer: (i) True; since the collection of real numbers is made up of rational and irrational numbers. (ii) False; as negative numbers cannot be expressed as the square root of any other number. (iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number. Question 2: 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. Answer: If numbers such as are considered, NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers are not irrational. intersecting number line at C. C is representing . perpendicular to OA. Then, taking O as centre and OB as radius, draw an arc Show how can be represented on the number line. Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length Question 3: Answer: We know that, And, Page 5 NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Class IX Chapter 1 – Number Sustems Maths Exercise 1.1 Question Is zero a rational number? Can you write it in the form , where p and q are integers ? 0? and q Answer: Yes. Zero is a rational number as it can be represented as etc. Question 2: Find six rational numbers between 3 and 4. Answer: There are infinite rational numbers in between 3 an d 4. 3 and 4 can be represented as respectively. Therefore, rational numbers between 3 and 4 are Question 3: NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Find five rational numbers between Answer: There are infinite rational numbers between . Therefore, rational are Question 4: State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number. Answer: (i) True; since the collection of whole numbers contains all natural numbers. (ii) False; as integers may be negative but whole numbers are positive. For example: -3 is an integer but not a whole number. (iii) False; as rational numbers may be fractional but whole numbers may not be. For example: is a rational number but not a whole number. numbers between . NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Exercise 1.2 Question 1: State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form , where m is a natural number. (iii) Every real number is an irrational number. Answer: (i) True; since the collection of real numbers is made up of rational and irrational numbers. (ii) False; as negative numbers cannot be expressed as the square root of any other number. (iii) False; as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number. Question 2: 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. Answer: If numbers such as are considered, NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers are not irrational. intersecting number line at C. C is representing . perpendicular to OA. Then, taking O as centre and OB as radius, draw an arc Show how can be represented on the number line. Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length Question 3: Answer: We know that, And, NCRTSOLUTIONS.BLOGSPOT.COM NCRTSOLUTIONS.BLOGSPOT.COM Exercise 1.3 Question 1: Write the following in decimal form and say what kind of decimal expansion each . Can you predict what the decimal expansion of are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of carefully.] Answer:Read More

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