The denominator is 2 cubed times 5, which equals 40. Since the highest power between the prime factors 2 and 5 is 3, the terminating decimal expansion will have exactly 3 decimal places.
A rational number in its lowest form has denominator 2³ × 5. How many decimal places will its decimal expansion have? Explain your answer.
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The denominator of the rational number in its lowest form is given as 2 cubed times 5, which equals 8 times 5, or 40. A fraction with a denominator of the form 2 raised to m times 5 raised to n will always have a terminating decimal expansion. The number of decimal places is determined by the higher exponent of the prime factors 2 and 5. Since the exponent of 2 is 3, it will have exactly 3 decimal places.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/