Friday, March 08, 2013

Unit Conversions and Significant Figures

Getting around in science requires that you learn how to convert units and also know how (and when) to do your rounding. Here are some pointers/reminders:

(NOTE: The video forgot to round up at 09:57, but the rest of the video is good.)

The benefit of knowing how to do unit conversion is that you can - literally - switch between different units, so long as you know the appropriate conversion factor. Recently, I was trying to determine how many gallons of water were pumped from the ground each day on an average Michigan farm in the production of corn. I had the following information:
  • # Farms of >14 acres: 114 farms
  • # Irrigated acres: 9,899 acres
  • 2006 Estimated Water Withdrawn: 4.85 million gallons per day (MGD)
  • Average Farm Acreage: 179 acres/farm
I need a final unit of gallons per day/179 acre farm, which means that I can do the following unit conversion:

gpd/average farm = [(1,000,000 gallons/day)/# farms]/[irrigated acres/# farms]*179 acres/average farm
=[(1,000,000 gallons/day)/114 farms]/[9,899 irrigated acres/114 farms]*179 acres/average farm
=[42,543.86 gpd/farm]/[86.83 irrigated acres/farm]*179 acres/average farm
=489.95 gpd/irrigated acre*179 gpd/average farm
=87,700.78 gpd/average farm

Final Answer (with sig-figs): 87,700 gpd/average farm

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