We are converting \( \text{ cm}^2 \) to \( \text{ m}^2 \) and therefore the factor of conversion between \( \text{ cm} \) and \( \text{ m} \) is needed first.
Using Table 1 above, we have \[ 1 \text{ m} = 100 \text{ cm}\] Square both sides \[ (1 \text{ m})^2 = (100 \text{ cm})^2 \] Simplify \[ 1 \text{ m}^2 = 10000 \text{ cm}^2 \] which gives the factors of conversion \[ \displaystyle \frac{1 \text{ m}^2}{10000 \text{ cm}^2} = 1 \quad (I) \] or \[ \displaystyle \frac{10000 \text{ cm}^2}{1 \text{ m}^2} = 1 \quad (II) \] To convert \( 2450 \text{ cm}^2 \), we use use the factor of conversion (I) given by \( \displaystyle \frac{1 \text{ m}^2}{10000 \text{ cm}^2} \) because it has \( \text{ cm}^2 \) in the denominator which will cancel with the given \( \text{ cm}^2 \).
Write the given expression as
\( 2450 \text{ cm}^2 = 2450 \text{ cm}^2 \times \color{red}1 \)
Substitute \( \color{red} 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ m}^2}{10000 \text{ cm}^2} \) since it is equal to \( \color{red}1 \)

\( 2450 \text{ cm}^2 = 2450 \text{ cm}^2 \times \displaystyle \frac{1 \text{ m}^2}{10000 \text{ cm}^2} \)
Cancel \( \text{ cm}^2 \)
\( 2450 \text{ cm}^2 = 2450 \cancel{\text{ cm}^2} \times \displaystyle \frac{1 \text{ m}^2}{10000 \cancel{\text{ cm}^2}} \)
Simplify
\( 2450 \text{ cm}^2 = \displaystyle \frac{2450 \times 1 }{10000} \text{ m}^2 \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 2450 \text{ cm}^2 = 0.245 \text{ m}^2 } \]

We are converting \( \text{ m}^2 \) to \( \text{ km}^2 \) and therefore the factor of conversion between \( \text{ m} \) and \( \text{ km} \) is needed first.
Use the table above to write factor of conversion between \( \text{ m} \) and \( \text{ km} \) \[ 1 \text{ km} = 1000 \text{ m}\] Square both sides \[ (1 \text{ km})(1 \text{ km}) = (1000 \text{ m})(1000 \text{ m})\] and simplify \[ 1 \text{ km}^2 = 1000000 \text{ m}^2 \] which gives the factors of conversion of area with \( \text{ m}^2 \) in the denominator \[ \displaystyle \frac{1 \text{ km}^2}{1000000 \text{ m}^2} = 1 \] Convert using the above factor of conversion
\( 34590.5 \text{ m}^2 = 34590.5 \text{ m}^2 \times \displaystyle \frac{1 \text{ km}^2}{1000000 \text{ m}^2} \)
Cancel \( \text{ m}^2 \)
\( 34590.5 \text{ m}^2 = 34590.5 \cancel{\text{ m}^2} \times \displaystyle \frac{1 \text{ km}^2}{1000000 \cancel{\text{ m}^2}} \)
Simplify
\( 34590.5 \text{ m}^2 = \displaystyle \frac{34590.5 \times 1 }{1000000} \text{ km}^2 \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 34590.5 \text{ m}^2 = 0.0345905 \text{ km}^2 } \]

Solutions to the Above Questions

1.      Convert \( 569000 \text{ mm}^2 \) to \( \text{m}^2 \)
   Use Table 1 to write \[ 1 \text{ m} = 1000 \text{ mm}\] Square both side \[ (1 \text{ m})(1 \text{ m}) = (1000 \text{ mm})(1000 \text{ mm})\] Simplify \[ 1 \text{ m}^2 = 1000000 \text{ mm}^2\] The above give the factor of conversion with \( \text{ mm}^2 \) in the denominator \[ \displaystyle \frac{1 \text{ m}^2}{1000000 \text{ mm}^2} = 1 \] Mutliply \( 569000 \text{ mm}^2 \) by the above factor of conversion
   \( 569000 \text{ mm}^2 = 569000 \text{ mm}^2 \times \displaystyle \frac{1 \text{ m}^2}{1000000 \text{ mm}^2}\)
   Cancel \( \text{ mm}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 569000 \text{ mm}^2 = 0.569 \text{ m}^2} \]
2.      Convert \( 1.2 \text{ km}^2 \) to \( \text{dam}^2 \)
   Use Table 1 to write \[ 1 \text{ km} = 100 \text{ dam}\] Square both side \[ (1 \text{ km})(1 \text{ km}) = (100 \text{ dam})(100 \text{ dam})\] Simplify \[ 1 \text{ km}^2 = 10000 \text{ dm}^2\] The above give the factor of conversion with \( \text{ km}^2 \) in the denominator \[ \displaystyle \frac{10000 \text{ dm}^2}{1 \text{ km}^2} = 1 \] Mutliply \( 1.2 \text{ km}^2 \) by the above factor of conversion to convert
   \( 1.2 \text{ km}^2 = 1.2 \text{ km}^2 \times \displaystyle \frac{10000 \text{ dm}^2}{1 \text{ km}^2} \)
   Cancel \( \text{ km}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 1.2 \text{ km}^2 = 12000 \text{ dam}^2} \]
3.      Convert \( 23.01 \text{ hm}^2 \) to \( \text{m}^2 \)
   Use Table 1 to write \[ 1 \text{ hm} = 100 \text{ m}\] Square both side \[ (1 \text{ hm})(1 \text{ hm}) = (100 \text{ m})(100 \text{ m})\] Simplify \[ 1 \text{ hm}^2 = 10000 \text{ m}^2\] The above gives the following factor of conversion with \( \text{ hm}^2 \) in the denominator \[ \displaystyle \frac{10000 \text{ m}^2}{1 \text{ hm}^2} = 1 \] Mutliply \( 23.01 \text{ hm}^2 \) by the above factor of conversion to convert
   \( 23.01 \text{ hm}^2 = 23.01 \text{ hm}^2 \times \displaystyle \frac{10000 \text{ m}^2}{1 \text{ hm}^2} \)
   Cancel \( \text{ hm}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 23.01 \text{ hm}^2 = 230100 \text{ m}^2} \]
4.      Convert \( 12.7 \text{ cm}^2 \) to \( \text{mm}^2 \)
   Use Table 1 to write \[ 1 \text{ cm} = 10 \text{ mm}\] Square both side \[ (1 \text{ cm})(1 \text{ cm}) = (10 \text{ mm})(10 \text{ mm})\] Simplify \[ 1 \text{ cm}^2 = 100 \text{ mm}^2\] The above gives the following factor of conversion with \( \text{ cm}^2 \) in the denominator \[ \displaystyle \frac{100 \text{ mm}^2}{1 \text{ cm}^2} = 1 \] Mutliply \( 12.7 \text{ cm}^2 \) by the above factor of conversion to convert
   \( 12.7 \text{ cm}^2 = 12.7 \text{ cm}^2 \times \displaystyle \frac{100 \text{ mm}^2}{1 \text{ cm}^2} \)
   Cancel \( \text{ cm}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 12.7 \text{ cm}^2 = 1270 \text{ mm}^2} \]
5.      Convert \( 13500 \text{ dm}^2 \) to \( \text{hm}^2 \)
   Use Table 1 to write \[ 1 \text{ hm} = 1000 \text{ dm}\] Square both side \[ (1 \text{ hm})(1 \text{ hm}) = (1000 \text{ dm})(1000 \text{ dm})\] Simplify \[ 1 \text{ hm}^2 = 1000000 \text{ dm}^2\] The above gives the following factor of conversion with \( \text{ dm}^2 \) in the denominator \[ \displaystyle \frac{1 \text{ hm}^2}{1000000 \text{ dm}^2} = 1 \] Mutliply \( 13500 \text{ dm}^2 \) by the above factor of conversion to convert
   \( 13500 \text{ dm}^2 = 13500 \text{ dm}^2 \times \displaystyle \frac{1 \text{ hm}^2}{1000000 \text{ dm}^2} \)
   Cancel \( \text{ dm}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 13500 \text{ dm}^2 = 0.0135 \text{ hm}^2} \]