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