How do I verify a conversion is correct?

Reverse the conversion by converting the result back using the reciprocal factor and confirm you recover the original value within rounding error.

Think of conversion like changing dollars to cents and back again to make sure you did it right; if you convert X units to Y units using a factor, then convert Y back to X using the reciprocal factor, you should end up with the same original number except for tiny differences from rounding. For example, if you multiply by three point five to go from A to B, divide by three point five to go from B back to A and check the number. Use enough decimal places when converting so rounding does not hide an error, and use the same unit definitions each time. If the number you get after reversing is very close to the original value, your conversion is correct; if not, you made a mistake in the factor, the arithmetic, or the units.

A common mistake is using the wrong conversion factor because you mixed up unit definitions, so always check that the factor matches the exact units and, if possible, derive the factor from known relationships rather than memory; another mistake is rounding too early which makes the reversed value differ noticeably, so keep extra decimal places through calculations and only round at the end; some students forget to use the reciprocal when reversing and instead apply the same factor twice, so remember reversing always uses the reciprocal of the original multiplier. A quick tip is to write the units through every step to catch swapped or missing units and to perform the reverse check immediately after the forward conversion.

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Verify Conversions by Reversing with Reciprocal

1. Reverse the conversion using reciprocal factor
2. Check you recover the original value
3. Allow tiny differences from rounding
4. Use enough decimal places when converting
5. Use consistent unit definitions each time

Common Conversion Mistakes to Avoid

1. Wrong conversion factor used
2. Rounding too early
3. Forgetting to use reciprocal

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