Question 6

After how many decimal places will the decimal expansion of 23/(2 4 × 5 3 ) terminate?

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Question 6 After how many decimal places will the decimal expansion of 23/(2^4 × 5^3 ) terminate? 23/(2^4 × 5^3 ) = 23/(2 × (2^3 × 5^3)) = 23/(2 × (2^3 × 5^3)) × 5/5 = (23 × 5)/(2 × 5 × (2^3 × 5^3)) = 105/((2^4 × 5^4)) = 105/(2 × 5)^4 = 105/(10)^4 = 0.0105 So, after 4 decimal places, the number will terminate

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.