Previous Year Question
The decimal equivalent of the number (4310)5, with base five as indicated is
Correct answer: D
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
(4310)5=4·125+3·25+1·5=580
Step-by-step solution
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.
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.
Quick method
Rightmost digit has power 0; powers increase moving left.