### Solution: Significant Figures

Conversion factors in red are exact

##### (1) Area, in acres, of a field that is 142.3 feet by 78.4 feet.

142.3 >> 4 sf

78.4 >> 3 sf

##### (2) Area in square meters covered by a rotating agricultural sprinkler that is 425 feet long.

425 >> 3 sf

##### (3) Volume of material in cubic yards removed from a 112.5 foot long rectangular trench that is 38 inches wide by 6.25 feet deep.

112.5 >> 4 sf

38 >> 2 sf

6.25 >> 3 sf

(4) Convert 18°12’47” to radians.

Step one - convert deg and min to seconds

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

64,800" | exact |

+720" | exact |

+47" | 2 sf |

65,567" | 5 sf |

Step three - convert the angle in seconds to radians

(5) Gravel for a road sub-base will be spread to a thickness of 6.0 inches 13.5 feet on both sides of centerline. What sub-base length in feet will covered by the gravel from a truck with a 12.4 cubic yard load?

6.0 >> 2sf

13.5 >> 3sf

12.4 >> 3sf

##### (6) A distance is measured in three segments by different surveyors. Their individual measurements are 3.45 meters, 7.83 feet, and 95.6 inches. What is the total distance in feet?

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

Step two - add the segments using sf addition rule

Step three - drop extra sf carried for intermediate comps

distance = 27.1 ft << 3 sf