Rounding And Significant Figures

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A chemistry assistant adds three measured volumes recorded as 12.4 mL, 6.25 mL and 0.0036 mL using graduated glassware. The sum should be reported correctly to how many decimal places?

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NCERT Class 11, Chapter 2 (Units and Measurements) gives a specific rule for addition and subtraction: the final result should be reported with the same number of decimal places as the measurement having the fewest decimal places. Among the three volumes, 12.4 mL has only one decimal place, 6.25 mL has two, and 0.0036 mL has four. The least precise value, 12.4 mL, governs the result, so the answer must be rounded to one decimal place. Two decimal places is wrong because it borrows precision from 6.25 mL, which the least precise term cannot support. Three decimal places is wrong as no measurement justifies thousandth-level certainty in the sum. Four decimal places is wrong since 0.0036 mL, though precise, is negligibly small and cannot raise the overall precision. A sanity check shows the tiny 0.0036 mL term barely affects the total, reinforcing that the coarse 12.4 mL reading limits the reported precision.

Rounding And Significant Figures

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