Transcript Chemistry by the numbers

Chemistry by the numbers
Units of Measurement – The Metric System
•
Length:
________ meter
•
Mass:
________ gram
•
Volume:
________
•
Temperature: _____ Celsius
•
Pressure: ____ atmosphere
liter
milli-
centi-
deci-
(unit)
deka-
hecta-
kilo-
0.001
0.01
0.1
1
10
100
1000
Chemistry by the numbers
Scientific Notation
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What is the mass of an electron?
0.000,000,000,000,000,000,000,000,000,000,911 kg
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What is the distance between our sun and Pluto?
5,913,520,000,000 m
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Is there a better way to write these numbers?
YES!
Chemistry by the numbers
Scientific Notation
First, locate the first significant digit
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Move this decimal...
...to just after the first
significant digit
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Then count the places the decimal moved...
Chemistry by the numbers
Scientific Notation
Your new number is then written times 10
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to the number of places you moved the decimal
kg
The number is negative because the original
number is a decimal
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So try it with the other number:
5,913,520,000,000 m →
Accuracy vs. Precision
Accuracy: measurements that are close to the
true value.
Precision: measurements that are consistent.
Significant Figures
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2 kinds of numbers:
–
Exact: The precise amount.
– (ie
–
Money in your pocket)
Approximate: Anything MEASURED.
–
No measurement is perfect
When to use Significant figures
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Scientists only use numbers that are
reliable.
Example:
The mass of a coin on a triple-beam balance is 2.7g
the mass of the same coin on a digital scale is 2.700g
Are they the same number?
When to use Significant figures
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To a mathematician, yes.
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To a scientist, No!
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2.700g to a scientist means the
measurement is accurate to within one
thousandth of a gram.
2.700g
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The digital scale is more accurate and
will have more significant figures.
How many sig figs?
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Rule 1: All numbers are significant starting
with the first non-zero digit on the left.
1st Exception: In whole numbers that end
in zero, the zeros at the end are not
significant.
???
Has 4 sig figs
Has 3 sig figs
Has 1 sig fig
How many sig figs?



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7
40
0.5
0.00003
7 x 105
7,000,000
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



1
1
1
1
1
1
How do I know how many?
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2nd Exception: Any zeroes between two
non-zero numbers are significant.
2002 sec
Has 4 sig figs
3rd Exception: Zeroes to the right of a
decimal are significant.
Has 6 sig figs
11.4000kg
4th Exception: decimal points make all
zeroes to the left significant.
Has 5 sig figs
90100. m
How do I know how many?
Sig Figs & Scientific Notation
Count all the numbers before the x10
9.3x10²cm =
2
4.1000x10³³kg =
5
How many sig figs?
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1.2
2100
56.76
4.00
0.0792
7,083,000,000
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
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2
2
4
3
3
4
How many sig figs?
3401
2100
2100.0
5.00
0.00412
8,000,050,000.
4
2
5
3
3
10
Sig Fig Calculations
When Adding or subtracting measurements
– Answer will have the same decimal place
as the least accurate number
–Ex: 2.45 cm + 1.2cm = 3.65cm?  3.7cm
– 1.2cm is least accurate so… round to the
one decimal
7.432L + 2L = 9.432L round to 9L
Sample Problems
123.0cm – 99.82cm =
2100.mL + 101mL =
88.772g – 17.1g =
24.00cm – 18cm =
7234.1m + 1000.0m =
708g – 8.4g =
23.2cm
2201mL
71.7g
6cm
8234.1m
700g
Sig Fig Calculations
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Multiplying or dividing, significant figures
Answer will have the same sig. figs as the
least reliable measurement.
56.780cm x 2.45cm = 139.111 cm2
5 sig figs
3 sig figs
Round to 3 sig figs...
139.111 cm2 → 139 cm2
If two numbers have the same reliability, use the least
amount of sig figs.
12.00km x 1.01km = 12.12km2
→ 12.1km2
Sample Problems
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1.0cm x 4cm =
4.00cm x 18cm =
7234.1m ÷ 100.0sec =
708g ÷ 8.1L =
298.01kg + 34.112kg =
84m/s x 31.221s =
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4cm²
72cm²
72.34m/sec
87.4g/L
332.12kg
2600 m