Transcript Sig Figs - wths

Significant
Figures
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Honors Chem section 1.5
Accuracy vs. Precision
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• Accuracy: how close a measured
value is to the true value.
• Precision: the degree of
reproducibility of a measurement. It
depends on how well you make a
measurement
These terms are often incorrectly used
interchangeably
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Examples
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• Your summer job is guessing people’s weights at
the traveling carnival
• Imagine you have one person who keeps
coming back and you guess their weights as:
• 56 kg • 65 kg • 70 kg • 51 kg
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• The average of these= 60.5kg
• If their actual weight is 60kg, the avg prediction
turns out to be accurate, but not precise
Examples
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• If instead you had made guesses of:
– 69kg -69kg -67kg -68kg
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• Your guesses would be precise, but not
accurate
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Precision
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• Precision can also mean how detailed the
number is
– Two Scales:
• Scale #1 = 180lbs
• Scale #2 = 180.49lbs
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– Which one is more precise?
– What is the difference in the scales?
Does that matter?
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• Mass of Obama
• Would it have been ok to report a time as 35
seconds instead of 35.14s?
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– Would have been OK, but not USEFUL for
Olympic competition
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• Could you have timed him so precisely with
an analog watch?
exactly
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• Exact #’s
– # of people in the room (counting #)
– 12 eggs/dz
– 1g = 1000mg
• Inexact #’s
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– #’s obtained by measurement
– Always have a level of uncertainty
Measuring
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• Measured quantities are reported in such a
way that only the last digit is uncertain
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• The number tells you what it was measured
with
measuring
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• Always estimate one digit further than the
measurement instrument gives (this is the
uncertain digit)
• Uncertainties of equipment are given as +/-
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+/- 0.01g
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+/- 0.1g
Significant Figures
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• The way we report numbers tells us how
we measured them…hence Significant
Figures
• All digits of a measured quantity,
including the uncertain one, are called
significant figures
• Not all #’s are significant, however – and
we will learn to count how many there are
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Examples – How Many Sig Fig’s are
In Each Number?
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The Rules
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• You’ll never find easier rules for significant figures than
these… trademarked at Tennent:
• 2 Conditions:
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– If there is a decimal point: Begin counting on
the right, and count numbers until there are no
more left, or you have hit all zeroes
– If there is no decimal point: Begin counting
on the left, and count numbers until there are
no more left, or you have hit all zeroes
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?
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• Which of the following is an inexact
quantity?
– A) the # of people in your math class
– B) the mass of a penny
– C) the # of grams in a kilogram
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?
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• Which of the following is an inexact
quantity?
– A) the # of people in your math class
– B) the mass of a penny
– C) the # of grams in a kilogram
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Uncertainty
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• Which measurement has more uncertainty?
What are the uncertainties?
26.1g
26.10g
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Uncertainty
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• Which measurement has more uncertainty?
What are the uncertainties?
26.10g
26.100g
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Special Conditions
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• Scientific Notation
• When numbers are written in Scientific Notation, all of the
numbers written are significant
• Counting Numbers
• Counting numbers are considered to have an infinite
number of sig figs (you’ll see the importance of this in
calculations)
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Calculations with sig figs
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Answers can only be as precise as the least
precise measurement
Addition/Subtraction
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Multiplication/Division
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The answer must have as many digits past the
decimal point as the number with the fewest digits
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The answer must have the same number of significant
figures as the number with the fewest sig figs
Use scientific notation when rounding is difficult
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43.2g + 51.0g + 48.7g = 142.9g
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258.3kg + 257.11kg + 253kg = 768.41kg
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0.0487m + 0.05834m + 0.00483m =
0.11187m
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5.236cm – 3.14cm = 2.096cm
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X&/
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24cm x 3.26cm = 78.24
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120m x 0.10lm = 12
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1.23m x 2.0m = 2.46
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60.2g / 20.1ml = 2.995024876
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Sig fig calculations
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• The result of adding 1.17 x 10-2 and 8 x 10-3
is, to the correct # of sig figs:
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A) 1.9 x 10-2
B) 1.97 x 10-2
C) 2.0 x 10-2
D) 0.02
E) none of the above
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Sig fig calculations
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• The result of adding 1.17 x 10-2 and 8 x 10-3
is, to the correct # of sig figs:
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A) 1.9 x 10-2
B) 1.97 x 10-2
C) 2.0 x 10-2
D) 0.02
E) none of the above
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Sig fig calculations
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• (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106
• the above calculation, when expressed to the
correct number of sig figs is:
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A) 4.4 x 106
B) 4.40 x 106
C) 4.41 x 106
D) 4.4090 x 106
E) 4.091 x 106
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Sig fig calculations
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• (107.36 – 99.2)(5.4033 x 105) = 4.4090928 x 106
• the above calculation, when expressed to the
correct number of sig figs is:
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A) 4.4 x 106
B) 4.40 x 106
C) 4.41 x 106
D) 4.4090 x 106
E) 4.091 x 106
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Density & Units
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