| S.No. | Number System |
| Concept (All formulas and definitions) |
| Exercise 1.1 |
| 1 | Is zero a rational number? Can you write it in the form p/q , where p and q are integers and q ≠0? |
| 2 | Find six rational numbers between 3 and 4. |
| 3 | Find five rational numbers between 3/5 and 4/5. |
| 4 | State whether the following statements are true or false. Give reasons for your answers. |
| Exercise 1.2 |
| 1 | State whether the following statements are true or false. Justify your answers. |
| 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. |
| 3 | Show how √5 can be represented on the number line.√5 = √(4+1) |
| Exercise 1.3 |
| 1 | Write the following in decimal form and say what kind of decimal expansion each has |
| 2 | You know that 1/7 = 0.142857 bar . Can you predict what the decimal expansion of 2/7 , 3/7 ,4/7 , 5/7 and 6/ 7 are, without actually doing the long division? If so, how? |
| 3 | Express the following in the form p/q , where p and q are integers and q ≠0. |
| 4 | Express 0.99999 .... in the form p/q .Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense. |
| 5 | What can the maximum number of digits be in the repeating block of digits in the decimal expansion of1/17? Perform the division to check your answer. Perform the division to check your answer. |
| 6 | Look at several examples of rational numbers in the form p / q (q ≠ 0), 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? |
| 7 | Write three numbers whose decimal expansions are non-terminating non-recurring. |
| 8 | Find three different irrational numbers between the rational numbers5/7 and9/11 |
| 9 | Classify the following numbers as rational or irrational: |
| Exercise 1.4 |
| 1 | Visualise 3.765 on the number line, using successive magnification. |
| 2 | Visualize 4.26 on the number line, up to 4 decimal places. |
| Exercise 1.5 |
| 1 | Classify the following numbers as rational or irrational: |
| 2 | 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 π is irrational. How will you resolve this contradiction? |
| 3 | Represent √9.3 on the number line |
| 4 | Rationalize the denominator of the followings |
| Exercise 1.6 |
| 1 | Find (i) 641/2 (ii) 321/5 (iii)1251/3 |
| 2 | find (i) 93/2 (ii)322/5 (iii)163/4 (iv)125-1/5 |
| 3 | Simplify : (i) 22/3.21/5 (ii)(1/33)7 (iii)111/2/111/4 (iv)71/2.81/2 |
