How do I convert between units using a conversion factor?

Use a conversion factor that equals one and arrange it so the units you do not want cancel, then multiply to get the desired units.

Think of unit conversion like trading stickers: you know how many small stickers make one big sticker, so you line them up to cancel the ones you do not want until only the one you do want is left. First write down the number with its unit, then multiply by a fraction made from an equivalence statement that has the unwanted unit on the top or bottom so it cancels with the original unit. Repeat with more conversion factors if you need several steps, always checking that units cancel across multiplication. The numerical answer comes from multiplying the numbers only after the units are arranged to cancel correctly.

A common mistake is choosing a conversion factor that is flipped the wrong way so the unwanted unit does not cancel, and the fix is to rewrite the fraction with the opposing numerator and denominator so the units match and cancel; another mistake is forgetting to use the units as guides and treating the process like pure number arithmetic, and the remedy is to write units next to every number and follow them through each step; a third mistake is rounding too early which makes the final answer less accurate, and the simple rule is to keep extra digits while working and round only at the end.

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Unit Conversion Using Conversion Factors

1. Line up units to cancel
2. Write number with its unit
3. Multiply by conversion fraction
4. Put unwanted unit opposite to cancel
5. Repeat for multiple steps
6. Check units cancel across multiplication
7. Multiply numbers after units arranged

Common Unit Conversion Mistakes

1. Using conversion factor flipped wrong way
2. Ignoring units during calculations
3. Rounding too early

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