How do I handle significant figures when converting units?

When converting units in chemistry, keep the same number of significant figures as the measured value unless the conversion factor is exact, in which case the conversion does not change the significant figures.

Think of significant figures like the count of trustworthy digits in a measurement, and conversion factors are just ways to change the label without making the measurement more or less precise when they are exact. If you have a measured length with three significant figures and you multiply or divide by an exact conversion factor, your result still has three significant figures because the exact number does not add uncertainty. If the conversion factor comes from a measurement with its own uncertainty, then treat it like another measured value and use the usual rules for multiplication and division to decide how many significant figures the final answer should have. When adding or subtracting converted values, align decimal places and round based on the least precise decimal place, not simply the count of digits.

Students often forget that defined conversions such as one hundred centimeters equals one meter are exact and do not limit significant figures; remember that exact numbers come from definitions or counts and do not carry uncertainty. Another common mistake is mixing rules for multiplication with rules for addition, which leads to wrong rounding; keep multiplication and division rules separate from addition and subtraction rules to avoid this. Some people also overround intermediate steps and lose precision, so keep extra digits during calculations and round only at the final answer.

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How to Handle Significant Figures When Converting Units

1. Count trustworthy digits in measurements
2. Exact conversions do not change precision
3. Measured conversions add uncertainty
4. Use multiplication/division sig-fig rules
5. Align decimals for addition/subtraction
6. Round based on least precise place
7. Keep extra digits until final

Common Mistakes with Significant Figures

1. Treating exact conversions as uncertain
2. Mixing multiplication and addition rules
3. Rounding intermediate calculation steps

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