How many sig figs for unit-conversion constants?

Keep at least as many significant figures in unit-conversion constants as the least precise measurement you are using; for distance conversions, using one point six zero nine three four four (six significant figures) is usually safe.

Think of significant figures like the number of digits you trust in a measurement, and when you multiply or divide by a conversion constant you do not gain extra precision, so you should keep the same number of trusted digits as your least precise input. If your measurement is to two significant figures, report the converted value with two significant figures; if your measurement is to five significant figures, keep five in the conversion result. Using a conversion like one point six zero nine three four four for miles to kilometers gives you six reliable digits, which covers most lab and homework needs without pretending to know more than you measured. Always carry a few extra digits through intermediate steps if you will round only at the end, then round the final answer to match the least precise input.

Many students mistakenly use every digit shown on a calculator result and report too many significant figures; the fix is to round the final answer to match the least precise input measurement. Another common error is thinking that exact defined constants like one hundred centimeters per meter have limited precision; those are exact so they do not limit significant figures, but measured values do, so treat exact conversions differently. A third mistake is dropping extra digits too early during calculations, which can introduce rounding error, so keep extra digits during work and only round the final reported result.

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How Many Sig Figs for Conversion Constants

1. Keep sig figs equal to least precise
2. Do not gain precision when converting
3. Match sig figs to measurement precision
4. Use 1.609344 for miles to km
5. Carry extra digits during calculations
6. Round final answer to match input

Common Sig Fig Mistakes in Conversions

1. Reporting too many significant figures
2. Treating exact conversions as limited precision
3. Rounding too early during calculations

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