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\( \left. \begin{array} { l }{ 2.5 cm ^ { 2 } = } \\ { 2.05 dm ^ { 2 } = } \\ { 20.5 m ^ { 2 } = } \\ { mm ^ { 2 } } \\ { cm ^ { 2 } } \\ { dm ^ { 2 } } \end{array} \right. \)

Ask by Evans Ryan. in Switzerland
Jan 16,2025

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Answer

2,5 cm² = 250 mm² 2,05 dm² = 205 cm² 20,5 m² = 2050 dm²

Solution

Gerne helfe ich bei den Umrechnungen der Flächeneinheiten: \[ \begin{array}{ll} 2{,}5\, \text{cm}^2 &= 250\, \text{mm}^2 \\ 2{,}05\, \text{dm}^2 &= 205\, \text{cm}^2 \\ 20{,}5\, \text{m}^2 &= 20{,}500\, \text{dm}^2 \\ \end{array} \] **Erklärung der Umrechnungen:** 1. **Von cm² zu mm²:** \[ 1\, \text{cm} = 10\, \text{mm} \quad \Rightarrow \quad 1\, \text{cm}^2 = (10\, \text{mm})^2 = 100\, \text{mm}^2 \] Also: \[ 2{,}5\, \text{cm}^2 \times 100 = 250\, \text{mm}^2 \] 2. **Von dm² zu cm²:** \[ 1\, \text{dm} = 10\, \text{cm} \quad \Rightarrow \quad 1\, \text{dm}^2 = (10\, \text{cm})^2 = 100\, \text{cm}^2 \] Also: \[ 2{,}05\, \text{dm}^2 \times 100 = 205\, \text{cm}^2 \] 3. **Von m² zu dm²:** \[ 1\, \text{m} = 10\, \text{dm} \quad \Rightarrow \quad 1\, \text{m}^2 = (10\, \text{dm})^2 = 100\, \text{dm}^2 \] Also: \[ 20{,}5\, \text{m}^2 \times 100 = 2050\, \text{dm}^2 \] Falls weitere Umrechnungen oder Erklärungen benötigt werden, stehe ich gerne zur Verfügung!

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Let's convert the area measurements into millimeters squared (mm²), centimeters squared (cm²), and decimeters squared (dm²) for you! 1. **Starting with the first conversion:** - \(2.5 \, \text{cm}^2\) = \(2.5 \, \text{cm}^2\) (it's already in cm²) - To convert to mm², remember that \(1 \, \text{cm} = 10 \, \text{mm}\) so, \[ 2.5 \, \text{cm}^2 = 2.5 \times 100 = 250 \, \text{mm}^2 \] 2. **Second part:** - \(2.05 \, \text{dm}^2\) = \(2.05 \, \text{dm}^2\) (already in dm²) - To convert to cm², \(1 \, \text{dm} = 10 \, \text{cm}\) hence, \[ 2.05 \, \text{dm}^2 = 2.05 \times 100 = 205 \, \text{cm}^2 \] - For mm², it will be \(205 \, \text{cm}^2 = 205 \times 100 = 20500 \, \text{mm}^2\) 3. **Lastly:** - \(20.5 \, \text{m}^2\) = \(20.5 \, \text{m}^2\) (already in m²) - To convert to cm², \(1 \, \text{m} = 100 \, \text{cm}\), \[ 20.5 \, \text{m}^2 = 20.5 \times 10,000 = 205000 \, \text{cm}^2 \] - For mm², it can be converted as follows: \(20.5 \, \text{m}^2 = 20.5 \times 1,000,000 = 20500000 \, \text{mm}^2\) So, in summary: - \(2.5 \, \text{cm}^2 = 250 \, \text{mm}^2\) - \(2.05 \, \text{dm}^2 = 20500 \, \text{mm}^2\) or \(205 \, \text{cm}^2\) - \(20.5 \, \text{m}^2 = 20500000 \, \text{mm}^2\) or \(205000 \, \text{cm}^2\) Can you see how a bit of metric conversion can greatly expand your spatial understanding? Just think of it like a magical tapestry where one unit weaves into another!

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