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CLASS – 9 MATHEMATICS. INTRODUCTION OF NUMBER SYSTEM.
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NUMBER SYSTEM It is a method of representing numbers..
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[image] Types of Number System Natural Numbers (N) NUMBER SYSTEM Whole Numbers (W) Integers (Z) Rational Numbers (Q) 01 Irrational Numbers Real Numbers (R) All Rational & Irrational Numbers Complex Numbers (C) a + ib (Example: 2 + 3i).
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2. Find five rational numbers between 3/5 and 4/5..
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4. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number..
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(iii) Every rational number is a whole number. False Rational numbers = 0, 19/30 , 2, 9/-3, -12/7… Whole numbers= 0,1,2,3…. All whole numbers are rational, however, all rational numbers are not whole numbers..
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4. Show how √5 can be represented on the number line. Sol. Step 1: AB = 2 unit Step 2: At B, draw a perpendicular line BC of length 1 unit. Step 3: Join CA Applying Pythagoras theorem, AB2+BC2 = CA2 22+12 = CA2 = 5 ⇒ CA = √5.
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5.Write the following in decimal form and say what kind of decimal expansion each has : (i) 36/100 Solution: = 0.36 (Terminating) (ii)1/11 Solution:.
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6.You know that 1/7 = 0.142857. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of 1/7 carefully.] Solution:.
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7.Express the following in the form p/q, where p and q are integers and q 0. (i) Solution: Let x = 0.666… Multiply both side by 10 10*x = 10*0.666… 10x = 6.666… 10x=6+0.666… 10x = 6 + x 10x-x =6 9x = 6 ; x = 6/9 x = 2/3.
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ii) 0.001 Solution: Assume that x = 0.001001… Multiply both side by 1000 1000*x = 1000*0.001001… 1000x = 1.001001… 1000x = 1 + x 1000x - x = 1 999x = 1 x = 1/999.
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8.Visualise 3.765 on the number line, using successive magnification..