A unit factor is a fraction made from two equal quantities expressed in different units that equals one and is used to convert from one unit to another.
Think of a unit factor like a magic helper that does not change the amount you have but changes the label on it. If you have one hour and want to know how many minutes that is, you multiply by the unit factor sixty minutes over one hour because sixty minutes equals one hour and the fraction equals one. Multiplying by one does not change the value, it only replaces the old unit with the new unit, so the number becomes easier to use for the problem. You can chain several unit factors to go from a tiny unit to a big unit or from a big unit to a tiny unit, just keep the unwanted units canceling out until only the unit you want is left.
Students often forget to line up the units so they cancel, which leaves the wrong unit in the answer; always write units above and below and cancel matching ones. Another common mistake is using a wrong conversion value like saying one liter equals one hundred milliliters instead of one thousand milliliters, so check the conversion facts before multiplying. Some students also multiply when they should divide or vice versa because they do not set the fraction equal to one correctly; if the unwanted unit does not cancel, flip the conversion factor so cancellation works.
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Unit Factor: Convert Units with One-Fraction
- Use a unit factor to convert
- Multiply by a fraction equal to one
- Example: 1 hr = 60 min
- Multiplying by one keeps value
- Chain factors to change units
- Cancel unwanted units as you go
Common Unit Factor Mistakes and Fixes
- Units not aligned for cancellation
- Using incorrect conversion values
- Multiplying instead of dividing
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