MP Board · Class 10 · Mathematics · Real NumbersThe decimal expansion of the rational number $13/3125$ will terminate after:
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Step-by-Step Solution
A rational number $p/q$ has a terminating decimal expansion if the prime factorization of $q$ is of the form $2^n 5^m$, where $n$ and $m$ are non-negative integers. Here, $3125 = 5^5 = 2^0 5^5$. Since the highest power of 5 is 5, the decimal expansion will terminate after 5 decimal places.
Detailed Options Breakdown
Option : 1 decimal place
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Option 1: 2 decimal places
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Option 2: 3 decimal places
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Real Numbers.
Option 3: 5 decimal places (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
💡 Study Guide: This question tests core syllabus concepts from Real Numbers. For formulas, key summaries, and mock exam reference guides, read the full Real Numbers Revision Notes.