Transcript Significant Figures

Significant Figures, and
Scientific Notation
The valid measurements or digits are
called SIGNIFICANT!
When using our calculators we
must determine the correct
answer; our calculators are
mindless drones and don’t know
the correct answer.
Significant figures are all the
digits in a measurement that are
known with certainty
plus a last digit that
must be estimated.
Uncertainties of Measurements
• Accuracy is the degree of “exactness” to
which the measurement quantity can be
reproduced.
Accuracy
• Is the extent to which a
measured value agrees
with the standard value
of the quantity.
• CALCULATORS DO
NOT INCREASE THE
ACCURACY!
Using Significant Figures
reflects precision by
estimating the last digit
What is the certain measurement? (52 ml)
What is the estimated measurement? (.8 ml)
The instrument determines the
amount of precision of the data.
What is the certain measurement here? (62.4 g)
What is the estimated measurement here? (.00 g)
Error vs. Mistakes
ERROR
• Scientific errors are
caused by
INSTRUMENTS
• Scientific
measurements vary
in their level of
certainty
MISTAKES
• Mistakes are
caused by
PEOPLE
• Misreading,
dropping, or other
human mistakes
are NOT error
Significant Digits
• Nonzero digits are always significant
• All final zeros after the decimal point are
significant
• Zeros between two other significant digits are
always significant
• Zeros used solely for spacing the decimal
point are not significant
Exact and Counting Numbers do
not have significant digits
Exact numbers are important:
they are infinitely valuable.
Counting numbers come only in
whole numbers.
There are rules for:
multiplication/division
addition/subtraction and
combined equations
Rules for multiplication/division
The result has the same number
of significant figures as the factor
with the fewest significant figures
The answer can’t be more precise
than the question
Rules for addition/subtraction
The result has the same number
of decimal places as the number
with the fewest decimal places
The answer can’t be more precise
than the question
1. Do the functions in
parenthesis
2. Note the number of significant
digits in the question
3. Perform the remainder of
calculations
4. Round the final answer
Calculations
• Addition/Subtraction • Multiplication/Division
• The answer is based on
the number with the
fewest decimal points
• The answer is based on
the number with the
fewest significant digits
Round only the
final answer in a
series of
calculations
Now You Try It!
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Add 24.686 m +2.343 m + 3.21 m = ?
Calculator says: 30.239
3 decimals, 3 decimals and 2 decimals
So 2 decimals it is
Answer is 30. 24 m
Multiply 3.22 cm by 2.1 cm
Calculator says 6.762
3 sig figs, 2 sig figs . . . So 2 it is!
Answer is 6.8 cm2
Divide .005673 L by 2.1 L
Calculator says 0.0027014286
4 sig figs and 2 sig figs
2 it is!
Answer is 0.0027 L
Scientific Notation
• In chemistry we often
use very large or very
small numbers
• We also have to pay
attention to significant
figures
• Scientific notation
allows us to do both
easily!
• Scientific Notation is using
powers of ten
• 1000 becomes
• 1 X 10 3
• 0.0001 becomes
• 1 X 10 -4
Try These
1. 34500
2. 0.00236
3. 56900000
3.45 x 104
2.36 x 10-3
5.69 x 107
4. 0.0000002386 2.386 x 10-7
How to do problems with
scientific notation
Ex. 4.7 x 10 25 x 1.9 x 10 -13
first do numbers: 4.7 x 1.9
estimate as 5 x 2 = 10
now do powers: 1025 x 10-13
25 + -13 = 12
so 10 x 1012 or 1.0 x 10 13
Calculators can help
First, type in the
number (ie 4.5)
Then press 2nd
Finally, press EE
(above the comma)
The number will display
as 4.5 E 13
Read this as 4.5 x 10 13
Significant figures are easy when
using scientific notation
2.3 x 10 25 has 2 sig figs
3.7 x 10 -30 has 2 sig figs
The placeholder zeros are
eliminated for you!