Why do we care about the units?
I bet the guys at NASA care!
Units and Conversions
Common Core
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Numbers/units are important to:
Ill-fated Mars Observer
One team of researchers
Used metric, the other
English units - resulting miscalculations caused the probe to burn up
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Mars
atmosphere © 2012 - The University or Arizona - HWR203
Water Issues
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Powers of Ten
Its perfectly acceptable (and often more common) to express
your answers using common powers of 10 abbreviations
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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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-
2.3 mg/L = .0023 g/L
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15.6 Maf = 15,600,00 af
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Scientific Notation & Sig.Figs.
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Examples
Sci. Notation format: x.xx * 10exp
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.
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:
0.01234
234,567
89.501 million meters
34.501 millimeters
Unless directed otherwise, express your answers to 3 sig.figs.
Sci. Notation format: x.xx * 10exp
http://antoine.frostburg.edu/chem/senese/101/measurement/sigfig-quiz.shtml
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Common Units – Relative sizes
Common Units – Kitchen
Equivalents
Relative Volumes
Equivalents
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
1.609 km = 1 mi
5280 ft = 1 mi
mL(ml)
t
T
oz
c
p
L
qt
gal
4.9 ml = 1 t
3t=1T
2 T = 1 oz
8 oz = 1 c
355 ml = 12 oz
2c=1p
2 p = qt
128 oz = 4 qt = 1 gal
3.8 L =1 gal
increasing
Relative Lengths
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Common Units – Weight
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Common Units – Field
Relative Weights
Equivalents
Relative Volumes
Equivalents
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
mL(ml)
L
gal
ft3
m3
ccf
af
1000 ml = 1 L
3.8 L = 1 gal
7.48 gal = 1 ft3
264 gal = m3
748 gal = ccf
1,234 m3 = 1 af
43,560 ft3 = 1 af
325,851 gal = 1 af
1 Mgal = 3.07 af
810 af = 1 Mm3
For water: ρw=1 g/cm3 = 1 g/ml = 1 kg/L = 1000 kg/m3
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New Units? - Volume
Units of Interest
Acre-foot
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:
It takes ~1000 m3 water
to produce ~ 1 ton of grain
Volume:
English units: [gal], [ft3], [acre-feet] or [af]
Metric units: [L], [m3], [Mm3]
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This is about the amount needed to
cover a football field with a foot of
water.
another fun fact
English units: [in2], [ft2], [mi2], acre[ac]
Metric units: [cm2], [m2], [km2], hectare[ha]
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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.
= 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.
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Acres & Hectares
10 ac
40 ac
USGS maps divided by
township & range
Each T/R is subdivided
into a 6x6 grid
Useful Equivalents Notation
Each map section is
1 square mile = 640 ac
1 ha = (100 m)2 = 100 m * 100 m =10,000 m2
Tucson street grid is:
Primary streets – every mile
ex. Speedway – Broadway
Campbell – Country Club
Secondary streets – every ½ mi
Ex. 5th St, Tucson
 So Sam Hughes is 160 ac
160 ac
Attention: common error!
(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
Metric: A hectare (ha = 2.47ac) is 100 m x 100 m
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Orders of Magnitude
What units do I use?
32 [M-af]
40
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]
1 [k-af]
1.2 [M-m3]
Volume of Chem-Bio
50 [af]
62 [k-m3]
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Annual
family use
0.5 [af]
620 [m3]
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Think about the idea of scale:
What units are appropriate for the volume of water in a:
(1) bucket?
(2) pond?
(3) reservoir?
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Performing unit conversions
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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”
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[B-m3]
Lake Mead
TAMA daily use
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What you don’t know
“Answer”
(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
10 [ft]
?[inch]
Which?
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Multiple conversions
Performing unit 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”
10 [ft]
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“Conversion”
*
12 [in/ft]
=
=
“Answer”
120 [in]
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Arizona Water Issues
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
Remember your basic area formulas:
height
width
Example: How many square feet are in one square meter?
Equivalents: 1 m2 = 10.76 ft2
base
Area = 1/2* base *height
Correct:
1[m2] *
(1 m)2 *
r
Area = Length * width
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Area
Area
Length
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Area = pi * r2; pi=3.1416
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10.76 [ft2/m2]
(1 [ft]/0.3048[m])2
=
=
10.76 [ft2]
10.76 [ft2]
1 [ft]/0.3048[m]
=
3.28 [ft-m]
Incorrect:
1[m2] *
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Volume
So volume is
a L3 term
Example: How many cubic centimeters are in 1 cubic meter?
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Sample problems
In performing unit conversions on volumes, a similar problem occurs
Remember how to
calculate the volume of a
cube
V=L*W*H
1 ft = 0.3048 m
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?
Equivalents: 1 m = 100 cm
Correct:
1 [m3] * (100 [cm]/[m])3
=
1,000,000 [cm3] = 106
Incorrect:
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1 [m3] *Issues
100 ([cm]/[m])
=- HWR203 100 [cm3]
4. How many gallons in a metric ton (1000 kg)
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Estimation
Estimating the volume of this room
Goals:
(1) Get a feel for how big these units are.
Team 1: Estimate the volume of this room.
(2) Understand how to estimate volumes.
What techniques can we
use to estimate the
dimensions of this room?
*Sometimes we do not have access to exact
measurements. How can we estimate the size
of a volume or area?
H
W
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Estimate the volume of the ILC
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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.
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