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Convert between metric units of length, area, and volume

Metric conversion involves recognizing that neighboring length units scale by powers of ten and using multiplication or division by the appropriate scale factor to express the same measurement in units such as millimeters, centimeters, meters, and kilometers. For area and volume, the conversion factor is squared or cubed respectively—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—rather than applying the length factor unchanged; conversions involving compound units or generalized dimensional systems are outside this scope.

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

Metric units are related by powers of (10)(10). For length,

1 m=100 cm.1\text{ m}=100\text{ cm}.

For area, the conversion factor must be squared because area has two dimensions:

1 m2=(100 cm)2=10,000 cm2.1\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2.

Example: Convert (2.4 m2)(2.4\text{ m}^2) to cm2\text{cm}^2

Step 1: Find the length conversion.

1 m=100 cm1\text{ m}=100\text{ cm}

Step 2: Square the conversion factor for area.

1 m2=1002 cm2=10,000 cm21\text{ m}^2=100^2\text{ cm}^2=10{,}000\text{ cm}^2

Step 3: Multiply by the area conversion factor.

2.4 m2×10,000=24,000 cm22.4\text{ m}^2\times 10{,}000 =24{,}000\text{ cm}^2

Therefore,

2.4 m2=24,000 cm2\boxed{2.4\text{ m}^2=24{,}000\text{ cm}^2}

Remember: use the length factor once for length, square it for area, and cube it for volume.

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

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