units and conversions - sahraweb.sahra.arizona.edu/.../lesson2b/hwr203units.pdf · arizona water...
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Units and Conversions
Common Core
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Arizona Water Issues
Why do we care about the units?I bet the guys at NASA care!
Ill-fated Mars ObserverOne team of researchersUsed metric, the otherEnglish units - resulting miscalculations caused the probe to burn up in Mars atmosphere
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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
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Powers of Ten
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109 = billion (B) giga-
106 = million (M) mega-
103 = thousand (k) kilo-
… … …
10-2 = (c) centi-
10-3 = (m) milli-
10-6 = (μ) micro-
10-9 = (n) nano-
Its perfectly acceptable (and often more common) to express your answers using common powers of 10 abbreviations
15.6 Maf = 15,600,00 af2.3 mg/L = .0023 g/L
Scientific Notation & Sig.Figs.
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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 * 10exp
Examples
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Sci. Notation format: x.xx * 10exp
http://antoine.frostburg.edu/chem/senese/101/measurement/sigfig-quiz.shtml
If your calculator says:
You should write it as: Shift decimal:
0.0002358 2.36 * 10-4 4 places to right
45,249.632 4.52 * 104 4 places to left
You try it:0.01234234,567
89.501 million meters34.501 millimeters
Common Units – Relative sizes
Relative Lengthsmmcminftydmkmmimi
Equivalents10 mm = 1 cm2.54 cm = 1 in
12 in = 1 ft3 ft = 1 yd
39.4 in ~ 1 m100 cm = 1 m
1000 m = 1 km1.609 km = 1 mi5280 ft = 1 mi
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incr
easi
ng
Common Units – Kitchen
Relative VolumesmL(ml)
tTozcpLqtgal
Equivalents4.9 ml = 1 t
3 t = 1 T2 T = 1 oz8 oz = 1 c
355 ml = 12 oz2 c = 1 p2 p = qt
128 oz = 4 qt = 1 gal3.8 L =1 gal
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Common Units – Weight
Relative Weightsmgglbkgkgton
metric ton
Equivalents1000 µg = 1 mg1000 mg = 1 g
454 g ~ 1 lb1000 g = 1 kg2.2 lb = 1 kg
2000 lb = 1 ton1000 kg = 1 metric ton
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For water: ρw=1 g/cm3 = 1 g/ml = 1 kg/L = 1000 kg/m3
Common Units – Field
Relative VolumesmL(ml)
Lgalft3
m3
ccfaf
Equivalents1000 ml = 1 L3.8 L = 1 gal
7.48 gal = 1 ft3
264 gal = m3
748 gal = ccf1,234 m3 = 1 af
43,560 ft3 = 1 af325,851 gal = 1 af1 Mgal = 3.07 af810 af = 1 Mm3
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Units of Interest
Time:seconds[s], minutes[min], hours[hr], days[d], years[yr]
Length:English units: inch[in], foot[ft], mile[mi]metric units: centimeter[cm], meter[m], kilometer[km]
Area:English units: [in2], [ft2], [mi2], acre[ac]Metric units: [cm2], [m2], [km2], hectare[ha]
Volume:English units: [gal], [ft3], [acre-feet] or [af]Metric units: [L], [m3], [Mm3]
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Arizona Water Issues
New Units? - VolumeAcre-footThe 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 m3 waterto produce ~ 1 ton of grain
= 264,000 gal = 0.81 af ~ 1100 ton water
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this is why it makes more sense to import
grain rather than water.
Arizona Water Issues
160 ac
40 ac
10 ac
USGS maps divided bytownship & range
Each T/R is subdividedinto a 6x6 grid
Each map section is1 square mile = 640 ac
Metric: A hectare (ha = 2.47ac) is 100 m x 100 m
Acres & Hectares
Tucson street grid is:Primary streets – every mileex. Speedway – BroadwayCampbell – Country Club
Secondary streets – every ½ miEx. 5th St, Tucson
So Sam Hughes is 160 ac
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Useful Equivalents NotationAttention: common error!
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1 ha = (100 m)2 = 100 m * 100 m =10,000 m2
(1 km)2 = (1000 m)2 = (103 m)2 = 106 m2
1 ac = (208.7 ft)2 = 43560 ft2
(1 m)3 = (100 cm)3 = (102 m)3 = 106 cm3
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Orders of Magnitude
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Lake Mead 32 [M-af] 40 [B-m3]
Annual Flow in Colorado 15 [M-af] 19 [B-m3]
Roosevelt Lake 3.8 [M-af] 4.7 [B-m3]
TAMA annual use 365 [k-af] 450 [M-m3]
TW CAP recharge 30 [k-af] 37 [M-m3]
TAMA daily use 1 [k-af] 1.2 [M-m3]
Volume of Chem-Bio 50 [af] 62 [k-m3]
Annual family use 0.5 [af] 620 [m3]
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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?
(3) reservoir?16© 2012 - The University or Arizona - HWR203
Arizona Water Issues
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 What you don’t know“Given” “Answer”
10 [ft] ?[inch]
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Performing unit conversions
(Step 2)How do you convert between these two measures? Look at your
table of Useful Equivalents under the particular measure of interest (Length) and find the appropriate equivalents.
In this case, the likely equivalents looks like this:1 ft = 12 in = 0.3048 m
Convert this into a fraction: either 1 ft/12 in or 12 in/ 1 ft
Which?
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Performing unit conversions
(Step 3): Multiply this by the Given value
“Given” “Conversion” = “Answer”10 [ft] * 12 [in/ft] = 120 [in]
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Multiple conversions
Most conversions are relatively straightforward, though they may require a few steps to complete
Example: How many seconds are in one day?
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AreaRemember your basic area formulas:
Area =
Length
width
Length * width
Area = 1/2* base *height base
height
r
Area = pi * r2; pi=3.1416
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Arizona Water Issues
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?
Equivalents: 1 m2 = 10.76 ft2 1 ft = 0.3048 m
Correct:1[m2] * 10.76 [ft2/m2] = 10.76 [ft2](1 m)2 * (1 [ft]/0.3048[m])2 = 10.76 [ft2]
Incorrect:1[m2] * 1 [ft]/0.3048[m] = 3.28 [ft-m]
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VolumeIn performing unit conversions on volumes, a similar problem occurs
Remember how to calculate the volume of a cube
V = L * W * HSo volume is
a L3 term
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Example: How many cubic centimeters are in 1 cubic meter?
Equivalents: 1 m = 100 cm
Correct:1 [m3] * (100 [cm]/[m])3 = 1,000,000 [cm3] = 106
Incorrect:1 [m3] * 100 ([cm]/[m])3 = 100 [cm3]
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Sample problems
Get together in groups of two to answer these questions:2. How many square miles (mi2) 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)
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Estimation
Goals:(1) Get a feel for how big these units are.
(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?
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Estimating the volume of this room
Team 1: Estimate the volume of this room.
What techniques can we use to estimate the dimensions of this room? H
WL
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Arizona Water Issues
Estimate the volume of the ILC
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Arizona Water Issues
Estimating the volume of the ILC(1)Get into groups of 4; half work inside; half outside
(2)Estimate the volume of the ILC (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 ILC by pacing, est. height
(6)Come back to class to pick up part two.28© 2012 - The University or Arizona - HWR203