Transcript Significant Figures, Scientific Notation, Unit Conversion

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SI units: The International System of Units
(abbreviated SI from the French Système
international d'unités]) is the modern form of the
metric system
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a system of units of measurement devised around
seven base units and the convenience of the number
ten
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1). Find your decimal
point
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2). Find your direction
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3). Count your steps
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4). Move the decimal
King Henry died by drinking chocolate milk
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Example: 12 Kilograms = _____ Decigrams
Deci is 4 spaces to the left of Kilo so move the
decimal 4 spaces to the right.
Answer: 12 kg = 120000 g
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I will give you these conversion factors if you
need them in a problem!
1 inch = 2.54 cm
exactly 1 lb = 454 g
1 qt = 0.946 L
1 mi = 5280 ft
1 qt = 2 pt
4qt = 1 gal
1 ounce = 28.349523 grams
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Convert 3598 grams into pounds.
(exactly 1 lb = 454 g )
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ANS: 7.925 lbs
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Convert 231 grams into ounces.
(1 ounce = 28.349523 grams)
ANS:8.15 ounces
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How many gallons are in 5.67 L?
(1 qt = 0.946 L and 4qt = 1 gal)
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ANS: 1.50
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Practice on your own
1). 5 decimeters =
2). 14 hL =
L
3). 245 kilograms=
4). 0.083 mm=
mm
mg
m
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Scientific notation is simply a method for
expressing, and working with, very large or
very small numbers.
-Numbers in scientific notation are made up of
three parts: the coefficient, the base and the
exponent.
-EX: 5.67 x103 is the scientific notation for 5670
-5.67 x 103
coefficient base exponent
1. The coefficient must be greater than or equal
to 1 and less than 10.
2. The base must be 10.
3. The exponent must show the number of
decimal places that the decimal needs to be
moved to change the number to standard
notation. A negative exponent means that the
decimal is moved to the left when changing to
standard notation.
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Move decimal until there’s 1 digit to its left.
-Places moved = exponent.
Large # (>1)  positive exponent
Small # (<1)  negative exponent
EX: Put 987000000000000000 in scientific
notation
Practice
Adding and Subtracting
 Be sure that the exponents are the same
 Then add or subtract the decimal
number as listed
Multiplication and Division
 To multiply – multiply the first factors then
add the exponents
 To divide – divide the first factors then
subtract the exponent of the divisor from the
exponent of the dividend
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Write the following numbers in scientific
notation
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Complete the following addition and
subtraction problems
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0.0045834 mm
438,904 s
6.23 x 106 kL + 5.34 x 107 kL
9.87 x 104 g – 6.2 x 103 g
Complete the following multiplication and
division problems
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(4.8 x 105 km) x (2.0 x 103 km)
(8.4 x 106 L) ÷ (2.0 x 103 L)
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Dimensional Analysis
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A tool often used in science for converting units within
a measurement system
Conversion Factor
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A numerical factor by which a quantity expressed in
one system of units may be converted to another
system
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The “Factor-Label” Method
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Units, or “labels” are canceled, or “factored” out
g
cm 

g
3
cm
3
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Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number.
4. Check units & answer.
How many seconds are in 1.4
days?
Plan: days
hr
min
seconds
1.4 days x 24 hr x 60 min x 60 sec =
1 day
1 hr
1 min
120960 sec
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Calculate density and use density to identify
pure substances
Ratio of mass to volume
 Directly proportional measure of how tightly matter
is packed
 Substances can be identified by comparing densities
to known densities
 density (D) = mass (m) / volume (V)
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 Expressed in g/mL
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Density can be calculated by measuring the change
in volume by a specifically measured mass
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A 5-mL sample of water has a mass of 5 g.
What is the density of water?
An object with a mass of 10 g raises the level of
water in a graduated cylinder from 25.1 mL to
30.1 mL. What is the density of the object?
The density of aluminum is 2.7 g/mL. What is
the volume of 8.1 g?
EQ: In what ways do proper
techniques contribute to reliable
results?
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Distinguish between accuracy and
precision in measurement
 Accuracy – extent to which a
measurement approaches the true
value of a quantity
 Agreement of a measurement
with the accepted value of the
quantity
 Precision – degree of exactness or
refinement of a measurement
 How close a series of
measurements are to one another.
France vs. Italy
Italy converts all five penalty kicks to win
championship
2005 Yr:
Att= 453 Comp=305
%Pass Completion= 305/453 = 67.3 %
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Calculating percent error
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% error = theoretical – actual x 100
theoretical
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The accepted length of a steel pipe is 5-m. Calculate
the percent error for each of these measurements
 5.25 m
 4.75 m
 5.5 m
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Rules recognizing significant figures
Non-zero numbers are always significant
 Zeros between non-zero numbers are always
significant
 All final zeros to the right of the decimal place are
significant
 Zeros that act as placeholders are not significant.
Convert quantities to scientific notation to remove
placeholder zeros
 Counting numbers and defined constants have an
infinite number of significant figures
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Rounding Rules
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If the digit to the immediate right of the last
significant figure is less than five, do not change the
last significant figure
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If the digit to the immediate right of the last
significant figure is greater than five, round up the
last significant figure
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If the digit to the immediate right of the last
significant figure is equal to five and is followed by a
nonzero digit, round up the last significant figure if
odd. If even, do not round up.
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How many significant figures in the following
measurements?
431,801 kg
 10,235.0 mg
 0.004384010 cm
 0.00986451cg
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Write the above in scientific notation to four
significant figures
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Rules for using significant figures in calculations
 Addition or Subtraction
 The answer can have no more digits to the right
of the decimal point than there are in the
measurement with the smallest number of digits
to the right of the decimal point
 10.03542 m
+12.02
m
22.05542 m = 22.06 m = 2.21 X 101 m
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Multiplication or Division
 The answer can have no more
significant figures than there are in
the measurement with the smallest
number of significant digits
Problem:
1.1135 g/mL x 500. mL = 556.75g
5.5675 x 102g = 5.57 x 102g
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Round the answers to each of the following
problems to the correct significant figures
7.31 x 104 + 3.23 x 103
 8.54 x 10-3 – 3.41 x 10-4
 (2.4 x 102) x (3.26 x 104)
 (1.024 x 102) ÷ (5.12 x 101)
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