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What You’ll Learn in this Unit Significant Figures Scientific Notation Measurement Dimensional
Analysis Error Density Graphical analysis
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Review of Measurement Terms Qualitative measurements -
words Quantitative measurements –
involves numbers (quantities) Depends on reliability of
instrument Depends on care with which it is
read
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Precision vs. Accuracy
Precision- the degree of agreement among several measurements of the same quantity.
Accuracy- the agreement of a particular value with the true value
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Uncertainty Basis for significant figures All measurements are
uncertain to some degree Random error - equal chance
of being high or low- addressed by averaging measurements - expected
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Significant Figures Meaningful digits in a
measurement The number of significant
figures in your measurement will tell the reader how exact the instrumentation used
If it is measured or estimated, it has sig figs.
If not it is exact (e.g. 5 apples).
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Significant Figures
All numbers 1-9 are significant. The problem are the ZEROS. Which ones count and which don’t? In between numbers 1-9 does Example: 4001……… has 4 sig
figs Now let me tell you a story…
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Left handed Archer
There once was a left handed archer who loved to shoot decimals. Zeros could not stop his arrow but numbers could.
If there is a decimal in the number begin on the left. Go through any zeros, come to the first number then all other numbers that follow are SIGNIFICANT!
→0.0040 →50.401
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No decimals
If a number has no decimals you begin on the right hand side.
Go through any zeros , come to the first number.
Then all numbers after that count
5000← 405,000 ←
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Doing the Math
Multiplication and division, same number of sig figs in answer as the least in the problem
Addition and subtraction, same number of decimal places in answer as least in problem.
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Scientific Notation
100 = 1.0 x 102
0.001 = 1.0 x 10-3
-- This provides a way to show significant figures.
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TOO QUICK FOR YOU!
So here are the rules.. slowly!1. Place decimal point after 1st
real non-zero integer. (ex) 1.0 NOT 10.0
2. Raise 10 to the exponential which equals the number of places you moved.
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Scientific Notation
The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)
Note: Moving the decimal to the left will
increase the power of 10 Moving the decimal to the right will
decrease the power of 10
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Sample Problems
2387 0.00007031 2900000000 0.008900 90100000 0.00000210
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Answers
2.387 x 103
7.031 X 10-5
2.9 x 109
8.900 X 10-3
9.01 X 107
2.10 X 10-6
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Scientific Notation Multiplication and Division
Use of a calculator is permitted use it correctly No calculator? Multiply the
coefficients, and add the exponents
(3 x 104) x (2 x 102) =
(2.1 x 103) x (4.0 x 10-7) =
6 x 106
8.4 x 10-4
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Scientific Notation
Multiplication and Division• In division, divide the coefficients,
and subtract the exponent in the denominator from the numerator
3.0 x 105
6.0 x 102= 5 x 102
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Scientific Notation
•Addition and Subtraction
•Before numbers can be added or subtracted, the exponents must be the same
•Calculators will take care of this
•Doing it manually, you will have to make the exponents the same- it does not matter which one
you change. (6.6 x 10-8) + (4.0 x 10-9) =
(3.42 x 10-5) – (2.5 x 10-6) =
7 x 10-8
3.17 x 10-5
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Measurement
Every measurement has two parts
Number with the correct sig - figs
Scale (unit) We use the
Systeme Internationale (SI).
COMMON SI UNITS
Symbol Unit Name Quantity Definition
m meter length base unit
kg kilogram mass base unit
s second time base unit
K kelvin temperature base unit
°Cdegree Celsius**
temperature
m3 cubic meter volume m3
L liter** volume dm3 = 0.001 m3
N newton force kg·m/s2
J joule energy N·m
W watt power J/s
Pa pascal pressure N/m2
Hz hertz frequency 1/s
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Metric Base Units
•Mass - kilogram (kg)•Length- meter (m)•Volume- (L)•Time - second (s)•Temperature- Kelvin (K)•Electric current- ampere (amp, A)•Amount of substance- mole (mol)•Energy – joule (j)
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Prefixesgiga- G 1,000,000,000 109
mega - M 1,000,000 106
kilo - k 1,000 103
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- 0.000001 10-6
nano- n 0.000000001 10-9
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Dimensional Analysis
Using Units to solve problems
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Dimensional Analysis
Use conversion factors to change the units
Conversion factors = 1 1 foot = 12 inches (equivalence
statement) 12 in = 1 = 1 ft.
1 ft. 12 in
2 conversion factors multiply by the one that will give you the
correct units in your answer.
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Example Problem
The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?
Well, we know that 1.00 ns = 10-9 seconds
(3.00 x 108 m) X (10-9 s) = 3.00 x 10-9 m/ns
s (1.00 ns)
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Example Problems
11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles.
How long is the race in rods, furlongs, meters, and kilometers?
A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?
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Volume
The space occupied by any sample of matter
Calculated for a solid by multiplying the length x width x height
SI unit = cubic meter (m3) Everyday unit = Liter (L), which is
non-SI
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Units of Mass Mass is a measure of the quantity of matter
Weight is a force that measures the pull by gravity- it changes with location
Mass is constant, regardless of location. The SI unit of mass is the kilogram (kg),
even though a more convenient unit is the gram
Measuring instrument is the balance scale
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Density Which is heavier- lead or feathers? It depends upon the amount of the
material A truckload of feathers is heavier than a small pellet of lead
The relationship here is between mass and volume- called Density
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Density Ratio of mass to volume D = m/V Common units are g/mL, or
possibly g/cm3, (or g/L for gas) Useful for identifying a compound Useful for predicting weight An intensive property- does not
depend on what the material is
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Things related to density density of corn oil is 0.89 g/mL
and water is 1.00 g/mL What happens when corn oil
and water are mixed? Why? Will lead float?
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Example Problem
An empty container weighs 121.3 g. Filled with carbon tetrachloride
(density 1.53 g/cm3 ) the container weighs 283.2 g. What is the volume of the container?
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Density and Temperature
What happens to density as the temperature increases? Mass remains the same Most substances increase in volume as temperature increases
Thus, density generally decreases as the temperature increases
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Density and water Water is an important
exception Over certain temperatures, the
volume of water increases as the temperature decreases
Does ice float in liquid water? Why?
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Specific Gravity
A comparison of the density of an object to a reference standard (which is usually water) at the same temperature Water density at 4 oC = 1 g/cm3
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Formula D of substance
(g/cm3) D of water
(g/cm3)• Note there are no units left, since they
cancel each other• Measured with a hydrometer • Uses?
• Gem purity• differentiating between different types of
crude oils/gasoline• urine tests for concentration of all chemicals
in your urine
Specific gravity =
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Temperature
Heat moves from warmer object to the cooler object Glass of iced tea gets colder?
Remember that most substances expand with a temperature increase?
Basis for thermometers
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Temperature scales
Celsius scale- named after a Swedish astronomer Uses the freezing point (0 oC) and boiling point (100 oC) of water as references
Divided into 100 equal intervals, or degrees Celsius
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Temperature scales
Kelvin scale (or absolute scale) Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius
No degree sign is used
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Temperature scales
Water freezes at 273 K Water boils at 373 K 0 K is called absolute zero, and
equals –273 oC
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Temperature
A measure of the average kinetic energy
Different temperature scales, all are talking about the same height of mercury.
In lab take the reading in ºC then convert to our SI unit Kelvin
ºC + 273 = K
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100ºC = 212ºF0ºC = 32ºF
100ºC = 180ºF1ºC =
(180/100)ºF1ºC = 9/5ºF
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Example problem
A 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol?
density 0.789 g/cm3 1 gal = 3.78 L
1 lb = 454 g
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Error Calculations
Error = Experimental value- accepted value
% error = [error] accepted value
X 100
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Graphing
The relationship between two variables is often determined by graphing
A graph is a “picture” of the data
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Graphing Rules – 10 items1. Plot the independent variable on the x-axis
(abscissa) – the horizontal axis. Generally controlled by the experimenter
2. Plot the dependent variable on the y-axis (ordinate) – the vertical axis.
3. Label the axis. Quantities (temperature, length, etc.) and
also the proper units (cm, oC, etc.)
4. Choose a range that includes all the results of the data
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Graphing Rules
5. Calibrate the axis (all marks equal)
6. Enclose the dot in a circle (point protector)
7.Give the graph a title (telling what it is about)
8. Make the graph large – use the full piece of paper
9. Indent your graph from the left and bottom edges of the page
10. Use a best fit line, do not connect points