number system

Question 3: Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c / d⋅ This seems to contradict the fact that π is irrational. How…

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Question 2: Simplify each of the following expressions: (i) (3+ √3)(2+ √2)  (ii) (3+ √3)(3− √3)  (iii) (√5+ √2)²  (iv) (√5− √2)(√5+ √2) Question 1 Question 3

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Question 1: Classify the following numbers as rational or irrational: (i) 2− √5    (ii)(3+ √(23))− √(23)    (iii) (2 √7) / (7 √7)    (iv) 1/ √2    (v) 2π Ex: 1.4 | Question 1 & 2 Question 2

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Question 1: Visualise 3.765 on the number line, using successive magnification. Question 2: Visualise 4.26 on the number line, up to 4 decimal places. Ex: 1.3 | Question 9 Ex: 1.5 | Question 1

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Example 9: Classify the following numbers as rational or irrational : (i) √(23) (ii) √(225) (iii) 0.3796 (iv) 7.478478… (v) 1.101001000100001… Question 7 & 8 Ex: 1.4 | Question 1 & 2

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Example 7: Write three numbers whose decimal expansions are non-terminating non-recurring. Example 8: Find three different irrational numbers between the rational numbers 5/7 and 9/11. Question 6 Question 9

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Example 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…

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Example 5: What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer. Question 4 Question 6

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Example 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. Question 3 Question 5

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