Transcript Conversions - Cashton Science

Scientific
Measurement,
Significant
Figures and
Conversions
Turning optical illusions
into scientific rules
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Types of measurement
Quantitative- use numbers to describe
 Qualitative- use description without
numbers
 4 feet
 extra large
 Hot
 100ºF
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Scientists prefer
Quantitative- easy check
 Easy to agree upon, no personal bias
 The measuring instrument limits how
good the measurement is
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How good are the
measurements?
Scientists use two words to describe
how good the measurements are
 Accuracy- how close the measurement
is to the actual value
 Precision- how well can the
measurement be repeated
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Differences
Accuracy can be true of an individual
measurement or the average of several
 Precision requires several
measurements before anything can be
said about it
 examples
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Let’s use a golf analogy
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Accurate? No
Precise? Yes
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Accurate? Yes
Precise? Yes
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Precise?
No
Accurate? Maybe?
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Accurate? Yes
Precise? We can’t say!
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In terms of measurement
Three students measure
the room to be 10.2 m,
10.3 m and 10.4 m across.
 Were they precise?
 Were they accurate?
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Significant figures (sig figs)
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How many numbers in a measurement
means something
When we measure something, we can (and
do) always estimate between the smallest
marks.
1
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2
3
4
5
Significant figures (sig figs)
The better marks the better we can
estimate.
 Scientist always understand that the last
number measured is actually an
estimate
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1
13
2
3
4
5
Sig Figs
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What is the smallest mark on the ruler that measures
142.15 cm?
One tenth of a cm
142 cm?
10 cm
140 cm?
100 cm
Here there’s a problem does the zero count or not?
They needed a set of rules to decide which zeroes
count.
All other numbers do count
Which zeros count?
Those at the end of a number before
the decimal point don’t count
 12400
 If the number is smaller than one,
zeroes before the first number don’t
count
 0.045
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Which zeros count?
Zeros between other sig figs do.
 1002
 zeroes at the end of a number after the
decimal point do count
 45.8300
 If they are holding places, they don’t.
 If they are measured (or estimated) they
do
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Sig figs.
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How many sig figs in the following
measurements?
458 g
3
4850 g
3
0.0485 g
3
40.0040850 g
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More Sig Figs
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Problems
50 is only 1 significant figure
 if it really has two, how can I write it?
 50.
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Adding and subtracting with
sig figs
The last sig fig in a measurement is an
estimate.
 Your answer when you add or subtract
can not be better than your worst
estimate.
 have to round it to the least place of the
measurement in the problem
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For example
27.93 + 6.4
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+
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First line up the decimal places
Then do the adding
27.93
Find the estimated
6.4
numbers in the problem
34.33 This answer must be
rounded to the tenths place
Rounding rules
look at the number behind the one
you’re rounding.
 If it is 0 to 4 don’t change it
 If it is 5 to 9 make it one bigger
 round 45.462 to four sig figs
 to three sig figs
 to two sig figs
 to one sig fig
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Practice
4.8 + 6.8765
 11.6765 = 11.7
 0.0045 + 2.113
 2.1175 = 2.118
 6.7 - .542
 6.158 = 6.2
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Multiplication and Division
Rule is simpler
 Same number of sig figs in the answer
as the least in the question
 3.6 x 653
 2350.8
 3.6 has 2 s.f. 653 has 3 s.f.
 answer can only have 2 s.f.
 2400
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Multiplication and Division
Same rules for division
 4.5 / 6.245
 0.720576461169 = 0.72
 4.5 x 6.245
 28.1025 = 28
 3.876 / 1983
 0.001954614221 = 0.001955
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Scientific Notation
Means to express a number in it’s
relation to 10’s
 Example: 8 x 102
 Rule:
Pos exponent = number bigger than zero
Neg exponent = number smaller than zero
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…Scientific Notation
8 x 102
Steps:
 Place a decimal behind the 8
 Pos or Neg? Move the decimal the
number of the exponent in the correct
direction, add the zeros
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8
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= 8 0 0 = 8 0 0 = 800
Scientific Notation
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Without a calculator
Sci. Not. – Multiplying and
Dividing
With exponents:
 Multiply the bases, then add the
exponents
 Divide the bases, then subtract the
exponents
 All answers MUST be in scientific
notation
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(2x103) x (4 x 105)
–2 x 4 = 8
–3 + 5 = 8
– 8 x 108
 (4x103) / (2 x 105)
– 4/2 =2
– 3-5= -2
– 2 x 10-2
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What if the answer isn’t in Sci.
Notation?
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(4x103) x (4 x 105)
– 4 x 4 = 16
–3+5=8
– 16 x 108
You must turn it into Sci. Notation
– If you move the decimal to the right,
subtract an exponent
– If you move the decimal to the left, add an
exponent
1.6 x 109
Sci. Not- Sub and Adding
A little more work:
– When adding decimals, the places
must be lined up
– Therefore, you cannot add two
numbers who have different
exponents
 (2 x 102) + (5 x 103) = 7 x 105
 200
+3000
3200
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You must change one exponent into the
other
 (2 x 102) + (5 x 103)
 Normal exponent rules apply
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(If you move the decimal to the right, subtract an exponent; If
you move the decimal to the left, add an exponent)
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Make sure your answer is in Sci. Not.
when you are finished
Measuring
The numbers are only half of a
measurement
 It is 10 long
 10 what.
 Numbers without units are meaningless.
 How many feet in a yard
 A mile
 A rod
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The Metric System
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AKA: SI system- International System of Units
Easier to use because it is a decimal system
Every conversion is by some power of 10.
A metric unit has two parts
A prefix and a base unit.
prefix tells you how many times to divide or
multiply by 10.
Base Units
Length - meter - m
 Mass - grams - g
 Time - second - s
 Energy - Joules- J
 Volume - Liter - L
 Amount of substance - mole – mol
 Temperature - Kelvin or ºCelsius K or C
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Prefixes
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Kilo K 1000 times
Hecto H 100 times
Deka D 10 times
deci d 1/10
centi c 1/100
milli m 1/1000
kilometer - about 0.6 miles
centimeter - less than half an inch
millimeter - the width of a paper clip wire
The Metric System
King Henry Died Drinking Chocolate
Milk
 KHD base dcm
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Other Prefixes
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Signify the powers of 10
Converting
k h D
d c m
how far you have to move on this chart,
tells you how far, and which direction to
move the decimal place.
 The box is the base unit, meters, Liters,
grams, etc.
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Conversions
k h D
d c m
Change 5.6 m to millimeters
starts at the base unit and move three to
the right.
move the decimal point three to the right
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56 00
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Dimensional Analysis
This is a structured way of helping you
to convert units, and solve problems.
 With this method, you can easily and
automatically convert very complex
units if you have the conversion
formulas.
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Using Conversion Factors
Make a fraction of the conversion
formula, to convert units.
 For a unit to cancel it must appear on
the top and the bottom of your
dimensional analysis problem.
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Steps for Conversion Factors
1.
2.
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6.
7.
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Rewrite the problem
What’s on top, goes on the bottom (as far
as labels go…)
What are you going to?
Which is bigger? The bigger unit gets a 1,
then fill in the rest of the numbers
Cancel like labels (if one’s on top and the
other’s on the bottom)
Check your labels to make sure you’re
finished
Do the math- Top: Multiply, Bottom: Divide
How To Use a Metric Ruler
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Contains centimeters and millimeters only.
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The larger lines with numbers are centimeters, and
the smallest lines are millimeters. Since millimeters
are 1/10th of a centimeter, if you measure 7 marks
after a centimeter, it is 1.7 centimeters long.
How to Use an English Ruler
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More difficult to read because they deal with
fractions
All rulers are marked with different markings
Link
Most are marked in 16ths.
Every mark is 1/16th of an inch.
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The center mark between numbers is 1/2.
The red lines on these rulers are marked at 1/2, and 1.
The next smallest marks on a ruler are 1/4ths.
The red marks on these rulers are at 1/4, 1/2, 3/4, and 1. (1/2 is
the same as 2/4)
The next smallest marks on a ruler are 1/8ths.
The red marks on these rulers are at 1/8, 1/4, 3/8, 1/2, 5/8, 3/4,
7/8, and 1.
The next smallest mark, if there are any, are 1/16ths.
The red marks on this ruler are at 1/16, 1/8, 3/16, 1/4, 5/16, 3/8,
7/16, 1/2, 9/16, 5/8, 11/16, 3/4, 13/16, 7/8, 15/16, and 1.
Let’s Try It with the
Smartboard!
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Density
how heavy something is for its size
 the ratio of mass to volume for a
substance
D=M/ V
 Independent of how much of it you have
 gold - high density
 air low density.
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Calculating
The formula tells you how
 units will be g/mL or g/cm3
 A sample of an unknown liquid has a
mass of 11.2 g and a volume of 23 mL
what is the density?
 11.2 / 23 = 0.49 g / ml
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Density Practice
A piece of wood has a density of 0.93
g/mL and a volume of 23 cm3 what is
the mass?
 0.93 = mass / 23 cm3
 21 grams
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Floating
Lower density floats on higher density.
 Ice is less dense than water.
 Most wood is less dense than water
 Helium is less dense than air.
 Water has a density of 1 g/ml
 A ship is less dense than water
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