Measurement Class 6
OB: To practice and master
dimensional analysis problems,
or unit conversion math
(with SF, density, etc.)
Take out your reference tables, calculators at the ready.
(1.06 Qt = 1 L)
Convert 2450 mL into gallons. Show all units (3 SF)
Convert 2450 mL into gallons. Show all units (3 SF)
2450 mL
1 Liter
1.06 Qt
1 gallon =
X 1000 mL X 1 Liter X 4 Qt
1
= 2597/4000 = 0.64925 gallons
= 0.649 gallons with 3 SF
How many millimeters are in 1000. yards?
Answer into scientific notation.
How many millimeters are in 1000. yards?
Put answer into scientific notation.
1000. yd
36 inch
2.54 cm
10 mm =
X 1 yd X 1 inch X 1 cm
1
= 914,400 mm = 9.144 x
With 4 SF
5
10
mm
If you have exactly 25.0 Liters of water, how
much does that weigh in tons?
Hint: write the density of pure water first, then see
if it helps you convert things around
If you have exactly 25.0 Liters of water, how
much does that weigh in tons?
The density of pure water is 1.0g per mL
which should tell you how much 25.0 liters mass is.
25.0 L X 1000 mL X 1 g X 1 pound X
1 mL
454 g
1L
1
1 ton
=
2000 p
= 25000/ 908000 = 0.0275 tons
with 3 SF
2.75 x 10-2 tons
In dimensional analysis, the units are there just
to be converted. They don’t “really” even matter.
In fact, they can be made up, make believe. As
long as you have equalities, you can convert from
one unit to another, even if they are fake units.
Using fake units is called abstract thinking. You
need to be abstract now, not obtuse. OK?
Imagine you are working at a zoo. Different
animals have different “values”, which are not
real, but come into play when trading other zoos
to get new cool animals. Think and get psyched
for this one…
You wish you could get a new proboscis monkey for the
empty cage at your zoo. You have an abundance of
lemurs on hand and hope to trade them away. In a
multi- zoo trade, you set it all up.
1 proboscis monkey = 14 zebras
8 zebras = 1 giraffe
2 giraffes = 1 elephant
1 elephant = 27 penguins
5 penguins = 1 lemur
If this is all true (it is, I promise), how many lemurs will it
take to get one proboscis monkey? (don’t sweat SF)
Round to the nearest whole lemur!
1 proboscis monkey = 14 zebras
8 zebras = 1 giraffe
2 giraffes = 1 elephant
1 elephant = 27 penguins
5 penguins = 1 lemur
1 proboscis monkey = 14 zebras
8 zebras = 1 giraffe
2 giraffes = 1 elephant
1 elephant = 27 penguins
5 penguins = 1 lemur
1 P.M. X 14 zebra
1 P.M.
1
1 lemur
27 penguins X
1 elephant
1 giraffe
X
X
X 1 elephant
5 penguins
2 giraffes
8 zebra
= 378/80 = 4.725 or
5 lemurs are equal to 1 proboscis monkey!
=
You have a special moment and discover a hunk of
metal in your yard in the dirt.
It’s stamped “pure osmium” and “100.0 grams”
as well. It looks pretty new and you even believe
this is real. What is the volume of this hunk of
metal in cm3? Show a formula and all your work.
SF are your initials.
Who would buy these?
You have a special moment and discover a hunk of metal in your
yard in the dirt.
It’s stamped “pure osmium” and “100.0 grams” as well. It looks
pretty new and you even believe this is real. What is the volume of
this hunk of metal in cm3? Show a formula and all your work.
D=
M
v
SF are your initials.
22.587 g/cm3
1
=
100.0 g
v
22.587 g/cm3 (v) = 100.0 g
v = 4.42732… = 4.427 cm3 with 4 SF
1.0 pigs equal 1.6 dogs
2.2 dogs is equal to 0.95 cats
1.9 cats is equal to 3.1 birds
1.0 bird is the same as 11.0 spiders
and finally, 3.7 spiders is the same as 8.5 bugs
If this is true, how many bugs make up 1.0 pig? (wow)
Please round (UP) to the nearest whole bug (or yuck!)
1.0 pig x
1
1.6 dog x
1.0 pig
0.95 cat x 3.1 birds x 11.0 spiders x 8.5 bugs
2.2 dogs
1.9 cats
1.0 birds
3.7 spiders
1.0 x 1.6 x 0.95 x 3.1 x 11.0 x 8.5 = 440.572
1 x 1.0 x 2.2 x 1.9 x 1.0 x 3.7 =
15.466
= 28.48648649 bugs
Rounded to the nearest whole bug, that’s 29 bugs!
Read the Measurement BASICS – NOTES due
Friday. Do the SF drills! Measurement Lab Friday.
Temperature lab ASAP.