We are given \( \text{ dam}^2 \), we therefore use Table 1 to find the conversion between \( \text{ dam} \) and \( \text{ hm} \). Using the Table 1 above, we have
\( 1 \text{ hm} = 10 \text{ dam} \)
Square both sides
\( (1 \text{ hm})(1 \text{ hm}) = (10 \text{ dam})(10 \text{ dam}) \)
Simplify and rewrite as
\( 1 \text{ hm}^2 = 100 \text{ dam}^2 \)
which gives the factor of conversion \[ \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} = 1 \]
Rewrite the given area \( 5680 \text{ dam}^2 \) as
\( 5680 \text{ dam}^2 = 5680 \text{ dam}^2 \times \color{red}1 \)
Substitute \( \color{red} 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} \) which is also equal to \( \color{red}1 \)

\( 5680 \text{ dam}^2 = 5680 \text{ dam}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} \)
Cancel \( \text{ dam}^2 \) on the right
\( 5680 \text{ dam}^2 = 5680 \cancel{\text{ dam}^2} \times \displaystyle \frac{1 \text{ hm}^2}{100 \cancel{ \text{ dam}^2}} \)
Simplify
\( 5680 \text{ dam}^2 = \displaystyle \frac{5680 \times 1 \text{ hm}^2 }{100} \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 5680 \text{ dam}^2 = 56.8 \text{ hm}^2 = 56.8 \text{ ha} } \]

We are given \( \text{ cm}^2 \), we therefore use Table 1 to find the conversion between \( \text{ cm} \) and \( \text{ hm} \)
\( 1 \text{ hm} = 10000 \text{ cm} \)
Square both sides
\( (1 \text{ hm})(1 \text{ hm}) = (10000 \text{ cm})(10000 \text{ cm}) \)
Simplify and rewrite as
\( 1 \text{ hm}^2 = 100000000 \text{ cm}^2 \)
which gives the factor of conversion \[ \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} = 1 \]
Rewrite the given area \( 125000 \text{ cm}^2 \) as
\( 125000 \text{ cm}^2 = 125000 \text{ cm}^2 \times \color{red}1 \)
Substitute \( \color{red} 1 \) by the factor of conversion \( \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} \) since it is equal to \( \color{red}1 \)

\( 125000 \text{ cm}^2 = 125000 \text{ cm}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100000000 \text{ cm}^2} \)
Cancel \( \text{ cm}^2 \)
\( 125000 \text{ cm}^2 = 125000 \cancel{ \text{ cm}^2} \times \displaystyle \frac{1 \text{ hm}^2}{100000000 \cancel{ \text{ cm}^2}} \)
Simplify
\( 125000 \text{ cm}^2 = \displaystyle \frac{125000 \times 1 \text{ hm}^2 }{100000000} \)
Evaluate
\[ \bbox[10px, border: 2px solid red] { 125000 \text{ cm}^2 = 0.00125 \text{ hm}^2 = 0.00125 \text{ ha} } \]

Solutions to the Above Questions

1.      \( 450000 \text{ m}^2 \) to \( \text{ ha} \)
   By definition
   \( 1 \text{ ha} = 10000 \text{ m}^2 \)
   The the factor of conversion between \( \text{ m}^2 \) and \( \text{ ha} \) is therefore given by
   \( \displaystyle \frac{1 \text{ ha}}{10000 \text{ m}^2} = 1\).
   Mutliply \( 450000 \text{ m}^2 \) by the above factor of conversion
   \( 450000 \text{ m}^2 = 450000 \text{ m}^2 \times \displaystyle \frac{1 \text{ ha}}{10000 \text{ m}^2} \)
   Cancel \( \text{ m}^2 \)
   \( 450000 \text{ m}^2 = 450000 \cancel{\text{ m}^2} \times \displaystyle \frac{1 \text{ ha}}{10000 \cancel{\text{ m}^2} } \)
   and evaluate \[ \bbox[10px, border: 2px solid red] { 450000 \text{ m}^2 = \displaystyle \frac{450000 \times 1 }{10000 } \text{ ha} = 45 \text{ ha} }\]
2.      Convert \( 4.5 \text{ km}^2 \) to \( \text{ ha} \)
   Using Table 1 above, we can write \[ 1 \text{ km} = 10 \text{ hm}\] Square both side \[ (1 \text{ km})(1 \text{ km}) = (10 \text{ hm})(10 \text{ hm})\] Simplify \[ 1 \text{ km}^2 = 100 \text{ hm}^2\] which gives the factor of conversion \[ \displaystyle \frac{100 \text{ hm}^2}{1 \text{ km}^2} =1 \] We now use the factor of conversion found above to write
   \( 4.5 \text{ km}^2 = 4.5 \text{ km}^2 \times \displaystyle \displaystyle \frac{100 \text{ hm}^2}{1 \text{ km}^2} \)
   Cancel \( \text{ km}^2 \) on the right
   \( 4.5 \text{ km}^2 = 4.5 \cancel{\text{ km}^2} \times \displaystyle \frac{100 \text{ hm}^2}{1 \cancel{\text{ km}^2}} \)
   and evaluate \[ \bbox[10px, border: 2px solid red] { 4.5 \text{ km}^2 = \displaystyle \frac{4.5 \times 100 }{1} \text{ hm}^2 = 450 \text{ hm}^2 = 450 \text{ ha}} \]
3.      Convert \( 550 \text{ dam}^2 \) to \( \text{ ha} \)
   Use Table 1 to write
   \( 1 \text{ hm} = 10\text{ dam}\)
   Square both side and simplify
   \( 1 \text{ hm}^2 = 100 \text{ dam}^2 \)
   which gives the factor of conversion
   \( \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} = 1 \)
   We now use the factor of conversion found above to write
   \( 550 \text{ dam}^2 = 550 \text{ dam}^2 \times \displaystyle \frac{1 \text{ hm}^2}{100 \text{ dam}^2} \)
   Cancel \( \text{ dam}^2 \) on the right
   \( 550 \text{ dam}^2 = 550 \cancel{\text{ dam}^2} \times \displaystyle \frac{1 \text{ hm}^2}{100 \cancel{\text{ dam}^2}} \)
   Evaluate \[ \bbox[10px, border: 2px solid red] { 550 \text{ dam}^2 = \displaystyle \frac{550 \times 1 }{100} \text{ hm}^2 = 5.5 \text{ hm}^2 = 5.5 \text{ ha} } \]
4.      Convert \( 8910000 \text{ mm}^2 \) to \( \text{ ha} \)
   Use Table 1 to write
   \( 1 \text{ hm} = 100000 \text{ mm}\)
   Square both side and simplify
   \( 1 \text{ hm}^2 = 10000000000 \text{ dam}^2 \)
   which gives the factor of conversion
   \( \displaystyle \frac{1 \text{ hm}^2}{10000000000 \text{ mm}^2} = 1 \)
   Mutliply \( 8910000 \text{ mm}^2 \) by the above factor of conversion
   \( 8910000 \text{ mm}^2 = 8910000 \text{ mm}^2 \times \displaystyle \frac{1 \text{ hm}^2}{10000000000 \text{ mm}^2} \)
   Cancel \( \text{ mm}^2 \) on the right
   \( 8910000 \text{ mm}^2 = 8910000 \cancel{\text{ mm}^2} \times \displaystyle \frac{1 \text{ hm}^2}{10000000000 \cancel{\text{ mm}^2}} \)
   Simplify and evaluate \[ \bbox[10px, border: 2px solid red] { 8910000 \text{ mm}^2 = \displaystyle \frac{8910000 \times 1 \text{ hm}^2}{10000000000} = 0.000891 \text{ ha} } \]
5.      Convert \( 900000 \text{ dm}^2 \) to \( \text{ ha} \)
   Use Table 1 to write \[ 1 \text{ hm} = 1000 \text{ dm}\] Square both side and simplify \[ 1 \text{ hm}^2 = 1000000 \text{ dm}^2\] The above gives the following factor of conversion \[ \displaystyle \frac{1 \text{ hm}^2}{1000000 \text{ dm}^2} = 1 \] Mutliply \( 900000 \text{ dm}^2 \) by the above factor of conversion to convert
   \( 900000 \text{ dm}^2 = 900000 \text{ dm}^2 \times \displaystyle \frac{1 \text{ hm}^2}{1000000 \text{ dm}^2} \)
   Cancel \( \text{ dm}^2 \) and evaluate \[ \bbox[10px, border: 2px solid red] { 900000 \text{ dm}^2 = 0.9 \text{ hm}^2 = 0.9 \text{ ha}} \]