# NCERT Solutions for Class 9 Maths

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# Number Systems

Exercise 1

1.    Is zero a rational number? Can you write it in the form , where p and q are integers and q ≠ 0?

2.    Find six rational numbers between 3 and 4.

3.    Find five rational numbers between .

Exercise 2

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.

5.    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.
6.    Show how √5 can be represented on the number line.

Exercise 3

7.   Write the following in decimal form and say what kind of decimal expansion each has:

8.   You know that Can you predict what the decimal expansions of are, without actually doing the long division? If so, how?

[Hint: Study the remainders while finding the value of  carefully.]

9.    Express the following in the form  where p and q are integers and q ≠ 0.

10.   Express 0.99999…. in the form  Are you surprised by your answer? Discuss why the answer makes sense with your teacher and classmates.

11.   What can the maximum number of digits be in the recurring block of digits in the decimal expansion of  Perform the division to check your answer.

12.    Look at several examples of rational numbers in the form  where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

13.   Write three numbers whose decimal expansions are non-terminating non-recurring.

14.   Find three different irrational numbers between the rational numbers

15.   Classify the following numbers as rational or irrational:

(i) 23             (ii) 225             (iii) 0.3796          (iv) 7.478478…

(v) 1.101001000100001…

Exercise 4

16.   Visualize 3.765 on the number line using successive magnification.

17.   Visualize  on the number line, up to 4 decimal places.

Exercise 5

18.   Write the following in decimal form and say what kind of decimal expansion each has:

19.   Simplify each of the following expressions:

20.  Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,  This seems to contradict the fact that g is irrational. How will you resolve this contradiction?

21.  Represent 9.3 on the number line.

22.  Rationalize the denominators of the following:

Exercise 6

23.  Find:

24.  Find:

25.  Simplify:

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