Significant Figures in Calculations

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where does the 0.0101 in solution come from? Shouldn't it be 0.01 *10 ^4?

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Yes, that is an error in the solution. Note that it doesn't affect the final result obtained.

Not sure where the error comes from, my guess would would be that a previous version of the problem had $1.01 \times 10^2$ as the first term. This was later changed (for whatever reason) and the solution only corrected in the first line, which just repeats the number in exactly the same form as the problem statement.