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# Questions on density, unit conversions and scientific notation

Submitted by Anonymous (not verified) on Sat, 03/08/2008 - 16:36

Acetone has a density of 0.791 g/mL. If 1 gallon = 3.7854 liters, how many kg should the
contents of a 5.00 gallon container filled with acetone weigh?
a. 1.045 kg
b. 12.6 kg
c. 13.8 kg
d. 15.0 kg
e. 23.9 kg

A number resulting from a measurement was properly expressed in scientific notation as 2.1 x 10-3 meters (m). The number could also be correctly written as
a. 0.0021 m
b. 0.002100 m
c. 0.00021 m
d. 2.1000 m
e. 21000 m

Given this data from lab, for mass and then the volume of water displaced in a graduated
cylinder by introduction of a metal sample to the cylinder.
Mass of weighing cup = 0.452 g.
Mass of weighing cup + metal sample = 72.943 g.
Volume of water in cylinder = 15.2 cm3.
When the metal sample was carefully lowered into the graduated cylinder, the water above the submerged metal sample rose to the 19.0 cm3 mark. What is the density of the metal?
a. 2.2 g cm-3
b. 3.8 g cm-3
c. 4.8 g cm-3
d. 19 g cm-3
e. 19.2 g cm-3

Thank you so much!!

Dimensional (unit) analysis allows us to set up conversion factors to  convert a value in one unit to a value in another unit.  The rule is that you have to put the unit you are going to on top, and the unit you are coming from on the bottom.

To convert feet to inches multiply by  a conversion factor with the units    (inches/foot)

The value of the numbers in the conversion fact have to be such that the quantity on top must equal the quantity on the bottom (that's why you can multiply something by a conversion factor because it has a value of 1)

So in the example above:      the conversion factor to convert from feet to inches would be:    (12 inches/1 foot)

Now in your first question decide what conversions you need to make to get to your final answer:

5 gal  ->  liters  ->  milliliters  -> grams  -> kg

Then come up with the conversion factors for each step:

5 gal  x  (3.7854 liters/ 1 gal)  x  ( 1000 mL / 1 L)  x  (.791 g/mL)  x  ( 1 kg/1000 g) =    ?  kg

Notice all of the units cancel except for kg, which is the unit that your answer is in.