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Check units in a solution

A solution is checked by verifying that each quantity has an appropriate unit and that the final unit answers the question—for example, lengths are not added to areas, and unlike units are converted before adding or subtracting. The reasoning includes interpreting products as measures such as square units and quotients as rates or unit rates, rather than treating units as labels that can be ignored. This scope uses familiar metric and customary units and straightforward conversions, not formal dimensional analysis of complex derived units.

Detailed Explanation: Check units in a solution

Before calculating, check that the units match what the operation requires.

Example: A rectangular rug is 22 meters long and (75)(75) centimeters wide. What is its area in square meters?

  1. Look at the units.
    The lengths use different units: meters and centimeters. Convert one so both measurements use the same unit.

  2. Convert centimeters to meters.
    Since (100 cm=1 m)(100\text{ cm}=1\text{ m}),

75 cm=0.75 m.75\text{ cm}=0.75\text{ m}.
  1. Use the area formula.
    Area of a rectangle is length times width:

A=(2 m)(0.75 m).A=(2\text{ m})(0.75\text{ m}).
  1. Multiply the numbers and the units.

A=1.5 m2.A=1.5\text{ m}^2.

The unit is m2\text{m}^2, or square meters, because a length in meters was multiplied by another length in meters.

  1. Check the answer.
    The question asks for area in square meters, and the final unit is m2\text{m}^2. The units match the question, so the answer is

1.5 square meters.\boxed{1.5\text{ square meters}}.

Do not multiply 22 and (75)(75) while leaving the units as meters and centimeters. Convert first so the measurements use the same unit.

Learn by doing: Check units in a solution

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Ratios - Unit Rates, Solve for Denominator


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