What is Chemistry
Chapter 1, Part 2
August 26th, 2004
How Good are My Numbers?
• Errors: Every measurement has an error that
accompanies it. Precision and accuracy indicate
the error.
• Precision: Measures how well same
measurements agree with each other.
• Accuracy: How close is the number to the actual
value? (Need to know the actual value of the
number).
• ACCURACY AND PRECISION ARE NOT THE
SAME!!!
26
Precision vs. Accuracy
Inaccurate and Imprecise
27
1
Precision vs. Accuracy
Inaccurate, but precise
28
Precision vs. Accuracy
Accurate and Precise!!!!
29
Significant Figures (Sig figs)
• Significant figures tell you how precise a certain
measurement is.
• Rules for significant figures:
– Read the digits from left to right.
– Start with the first non-zero number, count all digits.
10.45
1.00 x 103
1. x 102
0.015
1.0 x 102
100.
30
2
Special Rules for Zeroes
• Zeroes at the beginning of a number (called
leading zeroes) are NOT significant. 0.00123
has 3 significant figures.
• Zeroes between non-zero digits are ALWAYS
significant. 0.10203 has 5 significant figures.
• Zeroes at the end of a number (trailing zeroes)
containing a decimal point are ALWAYS
significant. 123.00 has 5 significant figures,
while 12300 has only 3 significant figures.
31
Exceptions to Rules for
Significant Figures
• Exceptions to the previous rules include
– Conversion factors
– Physical constants
– Special numbers like π and e
• Significant figures will change with any
mathematical operations being performed.
• In multi-step calculations carry all your sig figs
do not round off till the very end.
32
Exact Numbers
• A number that arises when items are counted
or units/conversion factors are defined.
– 45 students
– 12 eggs
– 1 inch = 2.54 cm
• In a calculation ignore the number of
significant figures in an exact number.
33
3
Addition/Subtraction
• Number of decimal places in the final answer
stays the same as the number with the lowest
number of decimal places. Consider:
34
Multiplication/Division
• Number of sig figs in the answer = number of
sig figs in the term with the lowest number of
sig figs. Consider:
35
Rounding off
• Round off 1.46, 1.44, 1.45 and 1.35 to 2 sig figs:
• 1.46 is rounded off to
– The last digit that is retained is increased by 1, if the digit
to the right of it is greater than 5.
• 1.44 is rounded off to
– Left unchanged, if the digit to the right of it is less than 5.
• 1.45 is rounded off to
– If the digit to its right is 5, then leave the retained digit
unchanged if it is even.
• 1.35 is rounded off to
– If the retained digit is odd, increase it by one.
36
4
Unit Conversions
• How many pesos will you get for 10 US
dollars?
• Need a conversion factor!! Here the relation
between dollars and pesos, one US dollar =
40 Mexican pesos:
37
Unit Conversions
• You win 4000 pesos and want to convert
them to US dollars;
• Now use the conversion factor 40 pesos = 1
US dollar
• We get:
38
Did you know
does math?
39
5
Conversion Factors
• Do not make up your own conversion factors!!
• Most conversion factors are tabulated.
• Always remember to use the conversion factor
so that the desired units are on top and are NOT
cancelled.
• Always setup so that:
40
Strategy for Unit Conversions
•
•
•
•
Identify where you want to go.
Choose the right starting point.
List the correct form of the conversion factors.
Multiply the starting measurement through by the
conversion factors.
• DOES THE ANSWER MAKE SENSE?
41
Common Variations
• Series of conversions
– How many seconds in one year?
• Converting powers of units and intersystem
conversions
– How many micrometers in 1.00 kilometer? How many
inches in 1.00 kilometer?
• Converting compound units
– The speed of light is 3.00 x 108 m/s. What’s this speed in
miles per hour?
• Starting point has to be constructed
– How many gallons of water will fill a 20.0 ft by 30.0 ft
rectangular swimming pool to a depth of 6.0 ft?
42
6
• Need to know the following:
• 1 year = 365 days
• 1 day = 24 hours
• 1 hour = 60 minutes
• 1 minute = 60 seconds
43
• Since 1 micrometer = 1 x 10-6 meter, there are 1 x 10+6
micrometers in 1 meter.
• 1 kilometer = 1 x 103 meter.
• Use these two conversion factors to set this up and pay
attention to the units here:
• This is an intersystem conversion and we need to use the
following conversion factors:
• 1 inch = 2.54 cm, 1 km = 103 m and 1 m = 102 cm
44
Speed of Light
• Here we have to work with each unit individually
and then put all our numbers together.
• For converting the meter to miles we will need
the following conversion factors:
– 1 mile = 1760 yards, 1 m = 1.094 yard.
– You may also use 1.608 km = 1 mile, though it would not
be very accurate.
45
7
Problem from the previous page continued
• Using 1 hour = 60 min and 1 minute = 60 s convert:
• Now combine this with information from the
previous slide to get:
46
Swimming Pool Problem
• We need to find the
volume required here by
multiplying the dimensions
of the pool. Thus:
• Volume = 20 ft x 30ft x 6ft
= 3600 ft3
– Since we are multiplying three
quantities in feet the answer
here has the units ft3.
• Now we have our starting
point:
47
• Convert the cubic feet to gallons by using the conversion
factors:
• 1 foot = 12 inches,
• 1 inch = 2.54cm,
• 1000 mL = 1L and
• 3.78 L = 1 gallon.
• This is a slightly tricky setup and keep track of how the units
change here.
• Also notice that I have cubed some conversion factors so they
cancel and it is perfectly acceptable to do this.
• Remember 1cm3 = 1mL.
48
8
Intersystem Conversions
• Very common problem.
• A recipe asks for 2.5 kg of ground beef. How
many grams of beef do I need? How many
pounds of beef should I buy? Convert kg to lb:
• Need to know: 1000 g = 1 kg and 454 g = 1 lb
49
9