When should you round during unit-conversion calculations?

Round only after completing all algebraic multiplication and division; do not round intermediate values, and round the final result to the precision required by the least precise measurement.

When you convert units, first write the full math with all multiplication and division using the exact numbers or values given, including conversion factors written out as fractions. Treat conversion factors as exact when they are defined that way, and carry all digits through the calculation without shortening them. Only once the arithmetic is finished should you round the final answer to match the number of significant figures required by the least precise measurement or by the problem statement. This keeps tiny rounding errors from building up and changing your answer.

Common mistakes are rounding every step because it feels simpler, which can change the final result, so avoid shortening numbers until the end; a quick fix is to use more digits in a calculator or keep numbers in fraction form until the final step. Another mistake is forgetting that some conversion factors are exact, like one meter equals one hundred centimeters, so they do not limit significant figures; remember to treat those as exact and only consider measurement uncertainty when counting significant figures. A final error is miscounting significant figures when measurements include zeros or are written in scientific notation, so double check the rules for leading zeros, captive zeros, and trailing zeros or rewrite numbers in scientific notation to make the correct count clear.

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When to Round in Unit Conversions

1. Do all multiplication and division first
2. Use exact conversion factors when defined
3. Carry all digits through calculations
4. Only round the final answer
5. Match precision to least precise measurement

Common Unit-Conversion Rounding Errors

1. Rounding intermediate steps too early
2. Treating exact conversion factors as uncertain
3. Miscounting significant figures with zeros

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