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Use conversion factors

Conversion factors represent equivalent measurements, such as 1 m=100 cm1\text{ m}=100\text{ cm}, as ratios equal to 1; multiplying by a suitable factor changes the numerical unit while preserving the quantity. The learner selects factors so unwanted units cancel, converts among common metric or customary units, and checks whether the result is reasonable, including conversions involving fractions or decimals. This scope excludes compound-unit conversions, temperature scales, and generalized dimensional analysis.

Detailed Explanation: Use conversion factors

A conversion factor is a fraction equal to 11 because its numerator and denominator name the same amount. For example,

1 m=100 cm1\text{ m}=100\text{ cm}

so both 100 cm1 m\frac{100\text{ cm}}{1\text{ m}} and 1 m100 cm\frac{1\text{ m}}{100\text{ cm}} equal 11.

To convert, multiply by the factor that makes the old unit cancel.

Example: Convert 2.52.5 meters to centimeters.

  1. Start with the measurement:

2.5 m2.5\text{ m}

  1. Choose a conversion factor with meters on the bottom, so m\text{m} cancels:

100 cm1 m\frac{100\text{ cm}}{1\text{ m}}

  1. Multiply and cancel the meters:

2.5 m×100 cm1 m2.5\text{ m}\times\frac{100\text{ cm}}{1\text{ m}} =2.5×100 cm=2.5\times100\text{ cm}

  1. Calculate:

=250 cm=250\text{ cm}

Therefore,

2.5 m=250 cm\boxed{2.5\text{ m}=250\text{ cm}}

This answer is reasonable because centimeters are smaller than meters, so the number should get larger.

Learn by doing: Use conversion factors

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    Measurement Conversion - Metric Mass Units (All) with Decimals - Large to Small

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