Transcript Scientific Measurements and Problem Solving

Chapter 3
Scientific measurement
1
Types of measurement
Quantitative- (quantity) use numbers to
describe
 Qualitative- (quality) use description
without numbers
 4 meters
Quantitative
 extra large Qualitative
 Hot
Qualitative
 100ºC Quantitative
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Which do you Think Scientists
would 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 word 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 anaolgy
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Accurate? No
Precise? Yes
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Accurate? Yes
Precise? Yes
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Precise?
No
Accurate? NO
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Accurate? Yes
Precise? We cant say!
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Reporting Error in Experiment
Error
• A measurement of how accurate an
experimental value is
• (Equation) Experimental Value – Accepted Value
• Experimental Value is what you get in the lab
• accepted value is the true or “real” value
• Answer may be positive or negative
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Reporting Error in Experiment
• % Error =
•
| experimental – accepted value | x 100
accepted value
OR
| error|
accepted value
• Answer is always positive
12
x 100
Example: A student performs an experiment
and recovers 10.50g of NaCl
product. The amount they should of
collected was 12.22g on NaCl.
1. Calculate Error
Error = 10.50 g - 12.22 g
= - 1.72 g
2. Calculate % Error
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% Error = | -1.72g | x 100
12.22g
= 14.08% error
Scientific Notation
2.5 is the coefficient
Example: 2.5x10-4 (___)
-4
and ( ___)
is the power of ten
Convert to Scientific Notation And Vise Versa
5.5 x 106
5500000 = ____________
0.0344
3.44 x 10-2 = ____________
2.16 x 103 = ____________
2160
1.75 x 10-3
0.00175 = ____________
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Multiplying and Dividing Exponents
using a calculator
9.00 x 102
(3.0 x 105) x (3.0 x 10-3) = _________________
2.475 x 1017
(2.75 x 108) x (9.0 x 108) = ________________
(5.50 x
(8.0 x
15
10-2)
108)
x (1.89 x
/ (4.0 x
10-23)
10-2)
-24
1.04
x
10
= ____________
10
2.0
x
10
= ________________
Adding and Subtracting Exponents
using a calculator
7.5 x
107
+ 2.5 x
109
9
2.575
x
10
= __________________
5.498 x 10-2
5.5 x 10-2 - 2.5 x 10-5 = _________________
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Significant figures (sig figs)
How many numbers mean anything
 When we measure something, we can
(and do) always estimate between the
smallest marks.
4.5 inches
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1
17
2
3
4
5
Significant figures (sig figs)

Scientist always understand that the last
number measured is actually an
estimate
4.56 inches
1
18
2
3
4
5
Sig Figs
What is the smallest mark on the ruler
that measures 142.15 cm? Tenths place
 142 cm? Ones place
 140 cm? Yikes!
 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
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Which zeros count?
Those at the end of a number before
the decimal point don’t count
 12400 = 3 sig figs
 If the number is smaller than one,
zeroes before the first number don’t
count
 0.045 = 2 sig figs
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Which zeros count?
Zeros between other sig figs do.
 1002 = 4 sig figs
 zeroes at the end of a number after the
decimal point do count
 45.8300 = 6 sig figs
 If they are holding places, they don’t.
 If they are measured (or estimated) they
do
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Sig Figs
Only measurements have sig figs.
 Counted numbers are exact
 A dozen is exactly 12
 A a piece of paper is measured 11
inches tall.
 Being able to locate, and count
significant figures is an important skill.
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Sig figs.
How many sig figs in the following
measurements?
 458 g = 3 sig figs
 4085 g = 4 sig figs
 4850 g = 3 sig figs
 0.0485 g = 3 sig figs
 0.004085 g = 4 sig figs
 40.004085 g = 8 sig figs
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Sig Figs.
405.0 g = 4 sig figs
 4050 g = 3 sig figs
 0.450 g = 3 sig figs
 4050.05 g = 6 sig figs
 0.0500060 g = 6 sig figs
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Question
50 is only 1 significant figure
 if it really has two, how can I write it?
 A zero at the end only counts after the
decimal place. 50.0 = 3 sig figs
 Scientific notation
 5.0 x 101
 now the zero counts.
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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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First line up the decimal places
27.93
+ 6.4
34.33
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Find the estimated numbers in
the problem
Then do the adding
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 = 45.46
 to three sig figs = 45.5
 to two sig figs = 45
 to one sig fig = 50
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Practice
4.8 + 6.8765 = 11.6756 = 11.7
 520 + 94.98 = 614.98 = 615
 0.0045 + 2.113 = 2.1175 = 2.118
 6.0 x 102 - 3.8 x 103 = 3198 = 3.2 x 103
 5.4 - 3.28 = 2.12 = 2.1
 6.7 - .542 = 6.158 = 6.2
 500 -126 = 374
 6.0 x 10-2 - 3.8 x 10-3= 0.0562 = 5.6 x 10-2
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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
practice
 4.5 / 6.245 = 0.720576 = 0.72
 4.5 x 6.245 = 28.1025 = 28
 9.8764 x .043 = 0.4246852 = 0.42
 3.876 / 1983 = 0.001954614 = 0.001955
 16547 / 714 = 23.17507 = 23.2
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The Metric System
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.
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Base Units
Length - meter more than a yard - m
 Mass - grams - a bout a raisin - g
 Time - second - s
 Temperature - Kelvin or ºCelsius K or C
 Energy - Joules- J
 Volume - Liter - half f a two liter bottle- L
 Amount of substance - mole - mol
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Prefixes
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
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Converting
K H D

d
c
m
King Henry Drinks (basically) delicious chocolate milk
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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Conversions
k h D
d c m
convert 25 mg to grams = 0.025 g
 convert 0.45 km to mm = 450,000 mm
 convert 35 mL to liters = 0.035 L
 It works because the math works, we
are dividing or multiplying by 10 the
correct number of times (homework)
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Volume
calculated by multiplying L x W x H
 Liter the volume of a cube 1 dm (10 cm)
on a side
 so 1 L =
 10 cm x 10 cm x 10 cm or 1 L = 1000 cm3
 1/1000 L =
3
 1 cm
 Which means 1 mL = 1 cm3
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Volume
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
1 L about 1/4 of a gallon - a quart

1 mL is about 20 drops of water or 1
sugar cube
weight is a
 force,
 Mass is the
 amount of matter.
 1gram is defined as the mass of 1 cm3
of water at 4 ºC.
 1 ml of water = 1 g
 1000 g =
 1000 cm3 of water
 1 kg = 1 L of water
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Mass
Mass
1 kg = 2.5 lbs
 1 g = 1 paper clip
 1 mg = 10 grains of salt or 2 drops of
water.
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Density
how heavy something is for its size
 the ratio of mass to volume for a
substance
M
D=M/V

D
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V
Density is a
Physical Property
 The density of an object remains
constant at constant
temperature
 _________
_______ ________
 Therefore it is possible to identify an
unknown by figuring out its density.

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Story & Demo (king and his gold crown)
What would happen to density if
temperature decreased?
As temperature decreases molecules
slow _____
down
 ______
 And come closer together therefore making
decrease
volume _________
STAYS ____
THE _______
SAME
 The mass ______
INCREASE
 Therefore the density would _______
WATER, because it expands.
 Exception _____________________
 Therefore Density decreases ICE FLOATS
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Units for Density
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1. Regularly shaped object in which a
g/cm3
ruler is used. ______

2. liquid, granular or powdered solid in
g/ml
which a graduated cylinder is used ______

3. irregularly shaped object in which the
water displacement method must be
used _____
g/ml
Sample Problem:
What is the density of a sample of
Copper with a mass of 50.25g and a
volume of 6.95cm3?
 D = M/V
 D = 50.25g / 6.95 cm3

= 7.2302 = 7.23 cm3
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Sample Problem 2.

A piece of wood has a density of
0.93 g/ml and a volume of 2.4 ml What
is its mass?
M
D
V
M=DxV
M = 0.93 g/ml x 2.4 ml
= 2.232 = 2.2 g
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Problem Solving or Dimensional Analysis
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Identify the unknown
What is the problem asking for
List what is given and the equalities needed to
solve the problem.
Ex. 1 dozen = 12
Plan a solution
Equations and steps to solve
(conversion factors)
Do the calculations
Check your work:
Estimate; is the answer reasonable
UNITS
All measurements need a NUMBER & A UNIT!!
Dimensional Analysis
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dimensions to help analyze
Use the units (__________)
solve the problem.
(______)
Conversion Factors: Ratios of equal measurements.
Numerator measurement = Denominator measurement
Using conversion factors does not change the value of the
measurement
12 in (_________)
equality
Examples; 1 ft = _____
1 ft__
12 in
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or
12 in
1 ft
(_____________
Conversion __________)
factors
What you are being asked to solve for in
the problem will determine which
conversion factors need to be used.
50

Common Equalities and their conversion factors:

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1 lb = _____oz

5280
1 mi = ______ft

1 yr = ______days
365

24
1 day = ____hrs

60
1 hr = ____min

60
1 min = ____sec
Sample Problems using Conversion Factors:
 How many inches are in 12 miles?
Equalities: 1 mi = 5280 ft
1 ft = 12 in
 12miles X 5280 ft X 12 in = 760,320
inches
1 ft
1 mi
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sig figs = 760,000 inches
2. How many seconds old is a 17 year old?

Equalities: 1 yr = 365 days; 1 day = 24 hrs;
1 hr = 60 min; 1 min = 60 sec

17 yrs X 365 day X 24 hrs X 60 min X 60 sec
1 yr
1 day
1 hr
1 min

= 536,112,000 sec

Sig figs = 540,000,000 sec
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3. How many cups of water are in 5.2 lbs of water?

Equalities: 1 lb = 16 oz; 8 oz = 1 cup
83.2
cup
16
oz
1
cup
 5.2 lbs X
X
=
8
1 lb
8 oz
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
= 10.4 cups

Sig figs = 1.0 x 101 cups
3. If the density of Mercury (Hg) at 20°C is 13.6 g/ml.
What is it’s density in mg/L?

Equalities: 1 g = 1000 mg; 1 L = 1000 ml
13.6 g X 1000 mg X 1000 ml =
1 ml
1g
1L
13,600,000 mg/L
13.6 x 107 mg/L
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