Question 11 - End-of-Chapter Exercises - Chapter 3 Class 9 - The World of Numbers (Ganita Manjari I)

Transcript

Question 11 Without performing division, determine whether the decimal expansion of 18/(125 ) is terminating or non-terminating. If it terminates, state the number of decimal places. A rational number 𝑝/𝑞 to be terminating decimal We check the prime factorisation of denominator If Denominator = q = 2n 5m where n ≥ 0 & m ≥ 0 Then, our fraction is terminating Let’s check 18/(125 ) Doing prime factorisation of denominator 125 = 5 × 5 × 5 = 53 Since it only contains 2s and 5s, it will be a terminating decimal Checking Number of Decimal Places To find the exact decimal value of a fraction without long division, we try to turn the denominator into a perfect power of 10 Now, our denominator is 125 = 53 To make power of 10, we multiply by 23 So that 53 × 23 = (5 × 2)3 Thus, 125 × 23 = 53 × 23 = (5 × 2)3 = 103 = 1,000 Since we have 3 zeros in denominator Our denominator terminates after 3 decimal places