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Base-5 to Decimal

The decimal equivalent of the number (4310)5, with base five as indicated is

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Answer & Explanation

Correct AnswerD. 580

Quick Explanation

Expand the base-5 number by positional weights: (4310)5=4×5³+3×5²+1×5+0=500+75+5=580. Therefore the decimal value is 580, option D.

Formula / Key Relation

(4310)5=4·125+3·25+1·5=580

Detailed Explanation

Correct Answer

D — 580

Concept and Reasoning

Expand the base-5 number by positional weights: (4310)5=4×5³+3×5²+1×5+0=500+75+5=580. Therefore the decimal value is 580, option D.

Calculation / Key Relation

(4310)5=4·125+3·25+1·5=580

Exam Takeaway

Rightmost digit has power 0; powers increase moving left.

Common Mistake

Do not read a base-5 numeral as an ordinary decimal number.

Quick Trick

Rightmost digit has power 0; powers increase moving left.

Common Mistake

Do not read a base-5 numeral as an ordinary decimal number.

Exam Tip

Rightmost digit has power 0; powers increase moving left.

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Exam Path

Knowledge Path

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QP-112-202425.pdf2024Q. 130

Base-5 to Decimal

Quick Explanation

Formula / Key Relation

Detailed Explanation

Correct Answer

Concept and Reasoning

Calculation / Key Relation

Exam Takeaway

Common Mistake

Quick Trick

Common Mistake

Exam Tip

Previous Exam Appearances

More Questions From This Concept

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