Saturday 20 April 2013

Number System

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

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