Transcript 1-6 Working with Numbers

1-6 Working with Numbers
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Significant Digits (sig fig's) - certain
digits and the estimated digit of a
measurement.
 Rules of Sig Fig's (Atlantic-Pacific
Rule)
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P of pacific stands for decimal
point present

If a decimal point is present you start on
the left side of the number, like the
pacific ocean is on the left side of
America. Read through the number
until you hit a non zero number. This
begins the significant numbers.
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A of Atlantic stands for decimal
point absent

If the decimal point is absent you begin
counting all non-zero digits from the
right or Atlantic side of the number.
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p. 47
Significant Figures Rules Table
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Rules for Significant
Zeros Animation
Examples
34.067g
 5 sig figs
 0.0007458ml
 4 sig figs
 0.009070g
 4 sig figs

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Examples
2030cm
 3 sig figs
 2007dm
 4 sig figs
 19,000,000,000g
 2 sig figs

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Practice Problems
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0.0026701m
 5 sig figs
19.0550kg
 6 sig figs
3500V
 2 sig figs
1,809,000L
 4 sig figs
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Sig Fig's in Calculations
Exact numbers or conversions do not count
as sig figs
 In multiplication or division the answer can
only have as many sig figs as the number
with the least amount of sig figs.
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Example: Volume = length x
width x height
Find the volume an object 10.876m x
1.34m x 13.22m
 on your calculator you will get a number
like 192.6661648
 The correct answer would be 193m3
 1.34m only has 3 sig figs
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
In addition or subtraction the largest
uncertainty determines the number of sig
figs
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Example
Add 34.50g + 3.2345g + 671.1g + 25.345g
= 734.7745g
 The largest uncertainty is 0.1 therefore
the answer could have one digit after
the decimal. The correct answer would
be 734.8g after rounding up
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Practice Problems
6.15m x 4.026m =
 12.7km / 3.0 =
 150ml + 76.9ml + 209ml + 0.036ml =
 (35.6L + 2.4L) / 4.803 =
 2.542m x (16.408m - 3.88m) =
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Scientific Notation
Mx
Greater than
or equal to 1
but less than 10
n
10
A whole number
A negative exponent means the number is small
A positive exponent means the number is large
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Scientific Notation
Example 19,000,000ml
 You can only have two sig fig's
 1.9 x 107
 Example 0.0004569g
 3 sig figs
 4.57 x 10-4g
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Sample Problems
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32,700
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 3.27 x 10
1,024,000
 1.024 x 106
0.0047100
-3
 4.7100 x 10
0.000000003901
 3.901 x 10-9
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Percent Error

% Error = measured – accepted x 100
accepted
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Sample Problem
In class Friday we calculated the density of
water. Many students reported values other
than the accepted value of 1g/ml or 1g/cm3
 Lets say you calculated the density of water
to be .9g/ml
 % Error = 0.9 - 1 x 100 = 10% error
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Density
 The
ratio of mass to volume
D = M / V
 Unit = kg/m3 or g/cm3 = g/mL
 A characteristic physical property
 Can be used to identify a substance
 Varies with temperature
Chapter 2 Section 2 Units of
Measurements pages 33-43
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p. 38
Density Table
Chapter 2 Section 2 Units of
Measurements pages 33-43
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Density Formula
Animation
Density
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2.
3.
What is the density of a block of marble
that occupies 310 cm3 and has a mass of
853 g?
Diamond has a density of 3.26g/cm3.
What is the mass of a diamond that has
a volume of 0.351 cm3?
What is the volume of a sample of liquid
mercury that has a mass of 76.2 g, given
the density of mercury is 13.6 g/mL?
p. 40
1. 2.75 g/cm3 2. 1.14 g 3. 5.60 mL
Chapter 2 Section 2 Units of
Measurements pages 33-43
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