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Significant Figures, Units,
Conversions, Density
Keep your brains on and your
calculators alert!
Significant Figure Rules
•Nonzero integers are significant
•Leading zeros are never significant
•Captive zeros are always significant
•Trailing zeros are only significant when
there is a decimal present in the number
•Exact numbers have an infinite number of
significant figures
Significant Figures
•60.0000
•400000
•7.023
•0.090
•0.0002
•3.05 x 105
Significant Figure Rules
for Addition and Subtraction
•The answer has the same
number of decimal places as the
least precise measurement.
7.2 + 4.841 =
3.142 - 1 =
Significant Figure Rules
for Multiplication and Division
•The number of SF in the
answer can be no greater than
the number of SF in value with
the least number of SF.
7.2 x 4.841 =
3.142 ÷ 1
=
Temperature Conversions
• Fahrenheit to Celsius:
(F  32F) x 5C / 9F
• Celsius to Fahrenheit:
(C x 9F / 5C) + 32F
Temperature Conversions
• Celsius to Kelvin:
• C + 273
• Kelvin to Celsius:
• K  273
How many SF are in the following:
a. 900.0
5
e. 6 x 10
b. 3.0020
f. 47,000
c. 6.020 x 10-2
g. 0.0001
d. 2007
h. 0.0098030
Round the following to 3 SF:
a. 900.0
5
e. 6 x 10
b. 3.0020
f. 47,000
c. 6.020 x 10-2
g. 0.0001
d. 2007
h. 0.0098030
Perform the following using applicable SF
rules:
a. 2.0 + 1.650
b. 12  0.00999
c.
-3
6
(8.040 x 10 ) x (9 x 10 )
d. 400  3.5
Measurement
•
•
•
•
•
mass--kg
length--m
time--s
temperature--K
amount of substance--mol
Measurement Prefixes
• giga(G)–
• mega(M)—10-6
• kilo(k)– 10-3
• hecto(h)– 10-2
• deka(da)– 10-1
-9
10
• deci(d)-• centi(c)-- 102
• milli(m)-- 103
• micro(µ)-- 106
• nano(n)-- 109
1
10
•Accuracy
•Precision
•Random error
•Systematic error
Metric-Metric Conversions
360 mm = _____m
4.25 x 10−5 ML = _____mL
325 mg = _____kg
Metric-English Conversions
360 mm = _____in
4.25 x 10−5 ML = _____gal
325 mg = _____lb
100 m/s = _____mi/h
Density
D = mass/volume
Vrectangular prism = l x w x h
Vcylinder = πr2h
Vsphere = (4/3)πr3
Density
A square piece of cobalt glass (glass with
cobalt ions mixed into it) has a mass of
12.228 g.
Its dimensions are 50 mm x50 mm x 2 mm.
What is its density in g/cm3?
Density
A cylindrical piece of aluminum metal has a
diameter of 12.5 mm and a mass of 16.559 g.
The density of aluminum is known to be 2.70
g/cm3.
What is its length in mm?
Density
A steel solid sphere has a diameter of 70
cm.
The density of this steel is known to be 7.80
g/cm3.
What is its mass in g?