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In an expression a×10^b,

Asked in JEE Main 8th April 1st Shift 2024 · Units and conversions

Answer: (2) b is order of magnitude for a≤5

Step-by-step solution

Idea: the order of magnitude is the power of ten nearest the number, so the mantissa a is rounded to the nearer of 1 and 10.

If a≤5 the mantissa rounds down to 1 and the order of magnitude stays b.

If a>5 the mantissa rounds up to 10, and 10×10^b=10^b+1, so the order becomes b+1.

So b is the order of magnitude when a≤5.

Why the other options are wrong

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