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Convert between metric units of length, area, and volume

Metric conversion preserves a quantity while changing its unit, using powers of ten among common metric units of length, area, and volume, including millimeters, centimeters, meters, kilometers, milliliters, and liters. Length conversion uses a scale factor once, while area and volume conversions use the factor squared or cubed (for example, 1 m2=10,000 cm21\text{ m}^2=10{,}000\text{ cm}^2 and 1 m3=1,000,000 cm31\text{ m}^3=1{,}000{,}000\text{ cm}^3); unit labels prevent confusing these relationships with ordinary decimal shifts. Rates, compound units, and generalized dimensional analysis are not included.

Detailed Explanation: Convert between metric units of length, area, and volume

To convert metric units, first find the conversion factor between the units. Then use that factor:

  • Length: use the factor once.
    1 m=100 cm1\text{ m}=100\text{ cm}
  • Area: square the factor.
    1 m2=(100 cm)2=10,000 cm21\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2
  • Volume: cube the factor.
    1 m3=(100 cm)3=1,000,000 cm31\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3

The unit label helps you remember whether to use the factor once, twice, or three times.

Example: Convert 0.04 m30.04\text{ m}^3 to cubic centimeters.

Since this is a volume conversion, cube the length conversion factor.

  1. Start with the basic length relationship:
1 m=100 cm1\text{ m}=100\text{ cm}
  1. Cube both sides:
1 m3=(100 cm)3=1,000,000 cm31\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3
  1. Multiply by 0.040.04:
0.04 m3×1,000,000=40,000 cm30.04\text{ m}^3\times 1{,}000{,}000 =40{,}000\text{ cm}^3

Therefore,

0.04 m3=40,000 cm3\boxed{0.04\text{ m}^3=40{,}000\text{ cm}^3}

For comparison, liters and milliliters use the relationship 1 L=1,000 mL1\text{ L}=1{,}000\text{ mL}. Always check the unit type before converting: length, area, and volume use different powers of the conversion factor.

Learn by doing: Convert between metric units of length, area, and volume

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    Measurement Conversion - Metric Volume Units (Common) with Decimals

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