Why do we care about the units? Units and Conversions. Powers of Ten. Numbers/units are important to: Scientific Notation & Sig.Figs.

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1 Why do we care about the units? I bet the guys at NASA care! Units and Conversions Common Core 1 Ill-fated Mars Observer One team of researchers Used metric, the other English units - resulting miscalculations caused the probe to burn up in Mars atmosphere 2 Numbers/units are important to: 1. Appreciate water quantities don t tune # s out! 2. Compare and understand usage amounts (agricultural, domestic, industrial; balances) 3. Estimate relative magnitudes of water resources (areas, volumes, flows) 4. Understand semi-technical topics and literature Powers of Ten Its perfectly acceptable (and often more common) to express your answers using common powers of 10 abbreviations 10 9 = billion (B) giga = million (M) mega = thousand (k) kilo = (c) centi = (m) milli = (μ) micro = (n) nano- 2.3 mg/ =.0023 g/ 15.6 Maf = 15,600,00 af 3 4 Scientific Notation & Sig.Figs. Significant Figures related to a number s precision. Important here mostly to avoid insignificant digits. Writing in scientific notation removes ambiguity related to leading or trailing zeroes. Unless directed otherwise, express your answers to 3 sig.figs. Sci. Notation format: x.xx * 10 exp If your calculator says: Examples Sci. Notation format: x.xx * 10 exp You should write it as: Shift decimal: * places to right 45, * places to left You try it: , million meters millimeters 5 6

2 Common Units Relative sizes Common Units Kitchen increasing Relative engths mm cm in ft yd m km mi mi 10 mm = 1 cm 2.54 cm = 1 in 12 in = 1 ft 3 ft = 1 yd 39.4 in ~ 1 m 100 cm = 1 m 1000 m = 1 km km = 1 mi 5280 ft = 1 mi Relative Volumes m(ml) t T oz c p qt gal 4.9 ml = 1 t 3 t = 1 T 2 T = 1 oz 8 oz = 1 c 355 ml = 12 oz 2 c = 1 p 2 p = qt 128 oz = 4 qt = 1 gal 3.8 =1 gal 7 8 Common Units Weight Relative Weights mg g lb kg kg ton metric ton 1000 µg = 1 mg 1000 mg = 1 g 454 g ~ 1 lb 1000 g = 1 kg 2.2 lb = 1 kg 2000 lb = 1 ton 1000 kg = 1 metric ton For water: ρ w =1 g/cm 3 = 1 g/ml = 1 kg/ = 1000 kg/m 3 9 Common Units Field Relative Volumes m(ml) gal ft 3 m 3 ccf af 1000 ml = = 1 gal 7.48 gal = 1 ft gal = m gal = ccf 1,234 m 3 = 1 af 43,560 ft 3 = 1 af 325,851 gal = 1 af 1 Mgal = 3.07 af 810 af = 1 Mm 3 10 Units of Interest New Units? - Volume Time: seconds[s], minutes[min], hours[hr], days[d], years[yr] ength: English units: inch[in], foot[ft], mile[mi] metric units: centimeter[cm], meter[m], kilometer[km] Area: English units: [in 2 ], [ft 2 ], [mi 2 ], acre[ac] Metric units: [cm 2 ], [m 2 ], [km 2 ], hectare[ha] Volume: English units: [gal], [ft 3 ], [acre-feet] or [af] Metric units: [], [m 3 ], [Mm 3 ] 11 Acre-foot The volume of water necessary to cover one acre to a depth of one foot. Equal to 43,560 cubic feet or 325,851 gallons or 1,234 cubic meters. This is about the amount needed to cover a football field with a foot of water. another fun fact It takes ~1000 m 3 water to produce ~ 1 ton of grain = 264,000 gal = 0.81 af ~ 1100 ton water this is why it makes more sense to import grain rather than water. 12

3 Acres & Hectares USGS maps divided by township & range Each T/R is subdivided into a 6x6 grid Useful Notation Attention: common error! 160 ac 40 ac 10 ac Each map section is 1 square mile = 640 ac Tucson street grid is: Primary streets every mile ex. Speedway Broadway Campbell Country Club Secondary streets every ½ mi Ex. 5 th St, Tucson So Sam Hughes is 160 ac Metric: A hectare (ha = 2.47ac) is 100 m x 100 m 13 1 ha = (100 m) 2 = 100 m * 100 m =10,000 m 2 (1 km) 2 = (1000 m) 2 = (10 3 m) 2 = 10 6 m 2 1 ac = (208.7 ft) 2 = ft 2 (1 m) 3 = (100 cm) 3 = (10 2 m) 3 = 10 6 cm 3 14 Orders of Magnitude ake Mead 32 [M-af] 40 [B-m 3 ] Annual Flow in Colorado 15 [M-af] 19 [B-m 3 ] Roosevelt ake 3.8 [M-af] 4.7 [B-m 3 ] TAMA annual use 365 [k-af] 450 [M-m 3 ] TW CAP recharge 30 [k-af] 37 [M-m 3 ] TAMA daily use 1 [k-af] 1.2 [M-m 3 ] What units do I use? Think about the idea of scale: What units are appropriate for the volume of water in a: (1) bucket? (2) pond? Volume of Chem-Bio 50 [af] 62 [k-m 3 ] (3) reservoir? 15 Annual family use 0.5 [af] 620 [m 3 ] 16 Performing unit conversions Performing unit conversions (Step 1) What units are you given? What units do you want to end up with? Write these down on the left and right sides of the paper, respectively. Example: How many inches in 10 feet? What you know Given What you don t know Answer 10 [ft]?[inch] (Step 2) How do you convert between these two measures? ook at your table of Useful under the particular measure of interest (ength) and find the appropriate equivalents. In this case, the likely equivalents looks like this: 1 ft = 12 in = m Convert this into a fraction: either 1 ft/12 in or 12 in/ 1 ft Which? 17 18

4 Performing unit conversions Multiple conversions Most conversions are relatively straightforward, though they may require a few steps to complete Example: How many seconds are in one day? (Step 3): Multiply this by the Given value Given Conversion = Answer 10 [ft] * 12 [in/ft] = 120 [in] Area Remember your basic area formulas: height ength Area Conversions for area can be a little tricky: In converting areas, it is critical to either use area to area conversions or to multiply by the length conversion factor twice Example: How many square feet are in one square meter? Area = width ength * width base Area = 1/2* base *height r Area = pi * r 2 ; pi= : 1 m 2 = ft 2 1 ft = m Correct: 1[m 2 ] * [ft 2 /m 2 ] = [ft 2 ] (1 m) 2 * (1 [ft]/0.3048[m]) 2 = [ft 2 ] Incorrect: 1[m 2 ] * 1 [ft]/0.3048[m] = 3.28 [ft-m] 22 Volume In performing unit conversions on volumes, a similar problem occurs Sample problems Remember how to calculate the volume of a cube V = * W * H So volume is a 3 term Example: How many cubic centimeters are in 1 cubic meter? : 1 m = 100 cm Correct: 1 [m 3 ] * (100 [cm]/[m]) 3 = 1,000,000 [cm 3 ] = 10 6 Incorrect: 23 1 [m 3 ] * 100 ([cm]/[m]) 3 = 100 [cm 3 ] Get together in groups of two to answer these questions: 2. How many square miles (mi 2 ) in 160 acres? 3. How many square feet in a hectare? 3. How many gallons are in one million cubic meters? 4. How many gallons in a metric ton (1000 kg) 24

5 Estimation Goals: (1) Get a feel for how big these units are. Estimating the volume of this room Team 1: Estimate the volume of this room. (2) Understand how to estimate volumes. *Sometimes we do not have access to exact measurements. How can we estimate the size of a volume or area? What techniques can we use to estimate the dimensions of this room? H W Estimate the volume of the IC Estimating the volume of the IC (1)Get into groups of 4; half work inside; half outside (2)Estimate the volume of the IC (order of magnitude) (3)Write this estimate down below your names. (4)Estimate your pace length of courtyard is 69 m (5)Team 2: Find the area of the IC by pacing, est. height (6)Come back to class to pick up part two