Open Access Surveying Library - Solution: Significant Figures

Conversion factors in red are exact

142.3 >> 4 sf

78.4 >> 3 sf

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

425 >> 3 sf

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

112.5 >> 4 sf
38 >> 2 sf
6.25 >> 3 sf

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

Step one - convert deg and min to seconds

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

Step two - add together the the angle parts to determine number of sf in the seconds

Step three - convert the angle in seconds to radians

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

6.0 >> 2sf
13.5 >> 3sf
12.4 >> 3sf

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

Step one - Convert all to feet carrying one additional sf.

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

Step two - add the segments using sf addition rule

$Area=142.3 ft \times 78.4 ft \times \left[ {\color{Red} \frac {1 ac} {43,560 ft^{2}}} \right ]\\\\ =0.256114\: ac =0.256\: ac\: \Leftarrow 3 sf$

Step three - drop extra sf carried for intermediate comps

distance = 27.1 ft << 3 sf