Scientific Notation, Percent Error, and Density

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SCIENTIFIC NOTATION, PERCENT
ERROR, DERIVED UNITS,
SPECIFIC GRAVITY
SECTION 2.1 AND 2.8
SCIENTIFIC NOTATION

Rules for placing numbers from standard form
into scientific notation:

Write all the significant digits of the numerical portion of
the value.

Move the decimal point in the numerical portion of the
value so there is ONE non-zero digit to the left of the
decimal point.

The number of places that the decimal point was moved
will be the power, or exponent, of 10 in the exponential
portion of the value.

Moving the decimal to the left is expressed as a positive
exponent, and moving the decimal to the right is
expressed as a negative exponent.
 Convert
the following numbers to
scientific notation.





24500
356
0.000985
0.222
12200.
 Convert
the following scientific notation
numbers to regular notation.





4.2 x 103
2.15 x 10-4
3.14 x 10-6
9.22 x 105
9.57 x 102
RULES FOR CALCULATIONS WITH
SCIENTIFIC NOTATION:
 For
addition and subtraction, convert to
ordinary notation before performing the
operation. This will allow you to correctly
count the number or decimal places needed
in your final answer.

For multiplication and division, your
calculator will put the answer into correct
scientific notation for you.
ROUNDING OFF:


Calculators will often present answers to
calculations with many more figures than the
significant ones. As a result many of the figures
shown are meaningless and the answer, before it
is presented, needs to be rounded off.
In a series of calculations always leave the
rounding off to the end, i.e. leave all numbers on
the calculator in the intermediate steps. Use the
simple rule that if the digit directly to the right of
the final significant figure is less that 5 then the
preceding digit stays the same, if it is equal to or
greater than 5 then the preceding digit should be
increased by one.

Compare your results to the literature
(accepted) value.
% Error =
% Error =

Your value - Literature value
Literature value
x 100%
Observed in Lab - Accepted from Literature
Accepted from Literature
Absolute value = ALWAYS POSITIVE!!!!!!
x 100%

All other units can be derived from base
quantities. This combination of base units is
called a derived unit.
Examples:
speed
length/time
volume (length) (length) (length)

m/s
m3
We will use volume measurements a lot, so it is
important to remember these relationships:
1 dm3 = 1L = 1000 mL = 1000 cm3
QUESTION:




Which is heavier a ton of
feathers or a ton of lead?
Neither, they both have the
same weight.
The better question would be
“Which is more DENSE?”
The lead is more dense.
DENSITY
Density =
mass
volume
Densitywater =
=
1.0 g/mL
g
mL or cm3
ARCHIMEDES – WATER DISPLACEMENT

Hiero II, king of Syracuse (a region in Greece)
during the 3rd century BC; commissioned the
production of a gold crown.
Suspected that he was being defrauded by
substituting a less precious metal in the interior.
 Hiero asked Archimedes to determine if the crown
was made of pure gold.


Could not damage or disassemble the crown.
 Non-destructive testing
Archimedes placed a block of pure
gold equal to the mass of the
crown in a container and filled it
to the brim with water.
He then removed the gold and
placed the crown in the container
and noticed that water
overflowed.
He concluded that the king was
cheated because the crown had
the same mass as the gold block,
but had a larger volume and
caused the water to overflow.
DENSITIES OF
COMMON
SUBSTANCES
WHAT DETERMINES WHETHER SOMETHING
WILL SINK OR FLOAT?
density of the object
 density of the liquid


Mercury is a liquid metal that has a density of
13.58 g/mL. Calculate the volume of mercury that
must be poured out in order to obtain 0.5 g of
mercury.
D =
m
V
V =
V =
0.5 g
m
D
mL
13.58 g
A 55.0 gal drum has a mass of 75.0 lbs.
when empty. What will the total mass be
when filled with ethanol?
density 0.789 g/cm3
55.0 gallon
drum
1 gal = 3.78 L
0.789 g
ethanol
1 cm3
1000 mL
3.78 L
1 kg
2.20 lb
1 cm3
1 mL
1L
1 gallon
1000 g
1 kg
= 360.87282 lbs of ethanol
= 75.0 lbs + 360.87282 lbs
= 435.87282 lbs
= 436 lbs
A 55.0 gal drum has a mass of 75.0 lbs.
when empty. What will the total mass be
when filled with ethanol?
density 0.789 g/cm3
55.0 gallon
drum
1 gal = 3.78 L
3.78 L
1000 mL
1 cm3
0.789 g
ethanol
1 kg
2.20 lb
1 gallon
1L
1 mL
1 cm3
1000 g
1 kg
= 360.87282 lbs of ethanol
= 75.0 lbs + 360.87282 lbs
= 435.87282 lbs
= 436 lbs
SPECIFIC GRAVITY

Specific gravity is a comparison of the density of a substance to the
density of a reference substance, usually at the same temperature.

Water is a convenient reference and is commonly used for this
measurement.
Specific Gravity =
Density of substance (g/cm3)
Density of water (g/cm3)

The units cancel, thus specific gravity has no units.

The specific gravity of a liquid can be measured with a hydrometer.

Physicians use specific gravity to measure a patient’s urine to
diagnose diabetes, while service stations use specific gravity to
determine the condition of the antifreeze in your car’s radiator

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