chapter 3 scientific measurement
DESCRIPTION
Chapter 3 Scientific Measurement. Anything in black letters = write it in your notes (‘knowts’). 3.1 – Using & Expressing Measurements. Measurements without units are useless!. “I walked 5 today.” “The speed of light is 186,000 “I weigh 890” “20 of water”. All measurements need units!. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 3Chapter 3
Scientific MeasurementScientific Measurement
Anything in black letters = write it in your notes (‘knowts’)
3.1 – Using & Expressing Measurements3.1 – Using & Expressing Measurements
Measurements without units are useless!
“I walked 5 today.”
“The speed of light is 186,000
“I weigh 890”
“20 of water”
All measurements need units!
We will often work with really large or really small numbers in this class.
872,000,000 grams
0.0000056 moles
= 8.72 x 108 grams
= 5.6 x 10-6 moles
Scientific Notation
6.02 x 1023
coefficient exponent
The coefficient must be a single, nonzero digit, exponent must be an integer.
Standard Notation
To multiply numbers written in scientific notation, multiply the coefficients and add the exponents.
(3 x 104) x (2 x 102) = (3 x 2) x 104+2 = 6 x 106
(2.1 x 103) x (4.0 x 10–7) = (2.1 x 4.0) x 103+(–7) = 8.4 x 10–4
Multiplication and Division
To divide numbers written in scientific notation, divide the coefficients and subtract the bottom
exponent from the top exponent.
2
5
10 x 0.6
10 x 0.3 2510 x 0.6
0.3
310 x 5.0210 x 0.5
Coefficient needs to be between 1 and 10
Addition and Subtraction
When adding or subtracting in Sci. Not., the exponents must be the same.
= (5.4 x 103) + (0.80 x 103)
(5.4 x 103) + (8.0 x 102)
= (5.4 + 0.80) x 103
= 6.2 x 103
Not the same, need to adjust one of the
exponents
Example
Solve each problem and express the answer in scientific notation.
a. (8.0 x 10–2) x (7.0 x 10–5)
b. (7.1 x 10–2) + (5 x 10–3)
a.
Multiply the coefficients and add the exponents.
(8.0 x 10–2) x (7.0 x 10–5)
= (8.0 x 7.0) x 10–2 + (–5)
= 56 x 10–7
= 5.6 x 10–6
b.
Rewrite one of the numbers so that the exponents match. Then add the coefficients
(7.1 x 10–2) + (5 x 10–3)
= (7.1 x 10–2) + (0.5 x 10–2)
= (7.1 + 0.5) x 10–2
= 7.6 x 10–2
Accuracy - closeness of a measurement to the actual or accepted value.
Precision - closeness of repeated measurements to each other
The closeness of a dart to the bull’s-eye corresponds to the degree of accuracy. The closeness of several darts to one another
corresponds to the degree of precision.
Good Accuracy, Good Precision
Poor Accuracy, Good Precision
Poor Accuracy, Poor Precision
Darts on a dartboard illustrate the difference between accuracy and precision.
Accuracy and Precision
Error
Suppose you measured the melting point of a compound to be 78°C
Suppose also, that the actual melting point value (from reference books) is 76°C.
The error in your measurement would be 2°C.
Error is the difference between the actual (accepted) and experimental value
How far off you are in a measurement doesn’t tell you much.
For example, lets say you have $1,000,000 in your checking account. When you balance your checkbook at the end of the month, you find that you are off by $175; error = $175
Now, lets be more realistic, you have $225 in your checking account and after balancing you are off by $175!
In both cases, there is an error of $175.
But in the first, the error is such a small portion of the total that it doesn’t matter as much as the second.
So, instead of error, percent error is more valuable.
Percent error compares the error to the size of the measurements.
ASSIGN: Chapter 3 Worksheet #1
Significant Figures
In any measurement, the last digit is estimated
30.2°CThe 2 is estimated (uncertain) by the experimenter, another person may say 30.1 or 30.3
0.72 cm
9.3 mL
Increasing Precision
The significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated.
Numbers that are NOT significant are called placeholders.
Rules for determining Significant Figures (p. 67)1. Every nonzero digit in a reported measurement is assumed to be significant.
2. Zeros appearing between nonzero digits are significant.
3. Leftmost zeros appearing in front of nonzero digits are not significant. They act as placeholders. By writing the measurements in scientific notation, you can eliminate such placeholding zeros.
4. Zeros at the end of a number and to the right of a decimal point are always significant.
5. Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are not significant if they serve as placeholders to show the magnitude of the number.
5 (continued). If such zeros were known measured values, then they would be significant. Writing the value in scientific notation makes it clear that these zeros are significant.
6. There are two situations in which numbers have an unlimited number of significant figures. The first involves counting. A number that is counted is exact.
6 (continued). The second situation involves exactly defined quantities such as those found within a system of measurement.
HOLY SMOKES!!
A shorter method for determining which numbers are significant in a measurement.
1.All nonzero numbers are significant.
2.Zeros are also significant if they are NOT placeholder zeros.
3.Counted and exact numbers have an unlimited number of sig figs.
The Tischer Method!™
A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.
Underline the zeros that are placeholders
100 1.00 0.23
0.0034 1.01 1005.4
0.10 100.0 54.0
A placeholder is a zero that ‘holds place’; it is only there to show how big or small a number is.
Zeros to the right of a number & after the decimal are more than placeholders, they are part of the measurement and are significant.
1. All nonzero numbers are significant.
2. Zeros are also significant if they are NOT placeholders.
3. Counted and exact numbers have an unlimited number of sig. figs.
How many significant digits are in the following measurements?
a) 150.31 grams b) 10.03 mL
c) 0.045 cm d) 4.00 lbs
e) 0.01040 m f) 100.10 cm
g) 100 grams h) 1.00 x 102 grams
i) 11 cars j) 2 molecules
“Box and Dot” Method for Counting Sig Figs
1. Draw a box around all digits from the 1st nonzero digit on left to last nonzero digit on the right.
2. If a dot is present, draw a box around any trailing zeros.
3. Any boxed digit is significant.
SOURCE: JCE Vol 86 No 8 (Aug ‘09) W. Kirk Stephenson
Another Shorter Method
An answer can’t be more accurate than the measurements it was
calculated from
Rules for Add/Subtracting Sig FigsThe answer to an +/- calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places.
3.2 cm
2.05 cm
+ 1.1 cm 3.15 cm
32.10 g
+ 5.0012 g 37.1012 g
37.10 g
Rules for Mult/Division Sig Figs The answer to a x/÷ calculation should be rounded to the same number of sig figs as the measurement with the least number of sig figs.
2.0 cm
x 1.89 cm 2 3.78 cm
3.8 cm2
8.19
8.1
g
mL 1.01111111... g mL
1.0 g mL
Always round your final answer off to the correct number of significant digits.
ASSIGN: Chapter 3 Worksheet #2
3.2 – Units of Measurement3.2 – Units of Measurement
SI Base Units (page 74)Quantity SI base
unitSymbol
Length meter m
Mass kilogram kg
Temperature kelvin K
Time second s
Amount of substance
mole mol
Luminous intensity
candela cd
Electric current
ampere A
SI – International System of Units
We will use all of these in this class
How is Mass different from Amount of Substance?
Commonly Used Metric Prefixes (page 75)Prefix Symbol Meaning Factor
mega M 1 million times larger than the base 106
kilo k 1000 times larger than the base 103
BASE Base Unit (meter, second, gram, etc)
deci d 10 times smaller than the base 10-1
centi c 100 times smaller than the base 10-2
milli m 1000 times smaller than the base 10-3
micro μ 1 million times smaller than the base 10-6
nano n 1 billion times smaller than the base 10-9
pico p 1 trillion times smaller than the base 10-12
Volume - Amount of space occupied by an object (remember?)
1 L = 1000 mL 1 mL = 1 cm3
Normal units used for volume:
Solids – m3 or cm3
Liquids & Gases – liters (L) or milliliters (mL)
The volume of a material changes with temperature, especially for gases.
Mass - Measure of inertia (remember?)
Weight - Force of gravity on a mass; measured in pounds (lbs) or Newtons.
Weight can change with location, mass does not
Energy – Ability to do work or produce heat.
Normal units used for energy:
SI – joule (J)
non-SI – calorie (cal)
How many joules are in a kilojoule?
How many calories are in a kilocalorie?
1 cal = 4.184 J
Temperature – measure of how cold or hot an object is.
Temperature – measure of the average kinetic energy of molecules.
Normal units used for temp:
SI – kelvin (K)
non-SI – celsius (°C) or Fahrenheit (°F)
K = °C + 273
yucky!
Celsius
Kelvin
100 divisions
100 divisions
100°CBoiling point
of water373.15 K
0°CFreezing point
of water273.15 K
Density is an intensive property
mass
volumeDensity =
Normal units for density:
g/cm3, g/mL, g/L
Densities of Some Common Materials
Solids and Liquids Gases
MaterialDensity at
20°C (g/cm3)Material
Density at 20°C (g/L)
Gold 19.3 Chlorine 2.95
Mercury 13.6 Carbon dioxide 1.83
Lead 11.3 Argon 1.66
Aluminum 2.70 Oxygen 1.33
Table sugar 1.59 Air 1.20
Corn syrup 1.35–1.38 Nitrogen 1.17
Water (4°C) 1.000 Neon 0.84
Corn oil 0.922 Ammonia 0.718
Ice (0°C) 0.917 Methane 0.665
Ethanol 0.789 Helium 0.166
Gasoline 0.66–0.69 Hydrogen 0.084
ASSIGN:
Read 3.2
Lesson Check 3.2; #23-35 (page 82)
3.3 – Solving Conversion Problems3.3 – Solving Conversion Problems
12 inches = ______ foot
1 minute = _____ seconds
10 cents = _______ dime
24 hours = ______ day
1 km = ________meters
4.184 Joules = _______ calorie
Fill in the blanks…
These can all be used as conversion factors
Conversion Factors
Any measurement that equals another measurement is a conversion factor
How to use conversion factors…to convert measurements…
1. Place the measurement you want to convert over 1.
2. Multiply by a conversion factor to cancel units.
Example 1
How many seconds are in 8 hours?
1.Start with given information.
2.Use conversion factors to cancel units until desired unit is left.
60 min = 1 hr; 60 sec = 1 min
Multiply across the top,
divide along the bottom of the conversion factors.
hours 8 x hour 1
minutes 60 xminute 1
seconds 60
seconds 28,800
Example 2
How many km are in 25 miles?
1.Start with given information.
2.Use conversion factors to cancel units until desired unit is left.
1.6 km = 1 mile
Multiply across the top,
divide along the bottom of the conversion factors.
miles 25 mile 1
km 1.6 x km 40
kmx 10 0.4 1
5.26 mumu = 8 nunu;
1.76 nunu = 12 fufu;
0.826 fufu = 1000 bubu.
1. How many mumus are in 10 bubus?
Example 3 – TRY IT!
2. How many fufus are in 26 mumus?
Example 4 – TRY IT!
5.26 mumu = 8 nunu;
1.76 nunu = 12 fufu;
0.826 fufu = 1000 bubu.
A student converted 10.1 feet as follows:
How many significant digits should the answer have?Why not 1?
ASSIGN:
Chapter 3 Worksheet 3
Conversion Factor QuizConversion Factor Quiz
1 horsepower = 745.7 W
2.54 cm = 1 inch
Show your WORK for credit.
LEFT: 1. Convert 6.5 horsepower into watts
RIGHT: 1. Convert 100 watts into horsepower
LEFT: 2. How many cm are in 12 miles?
RIGHT: 2. How many cm are in 20 miles
Practice With ConversionsPractice With Conversions
1 horsepower = 745.7 W
2.54 cm = 1 inch
Show your WORK for credit.
LEFT: 1. Convert 6.5 horsepower into watts
RIGHT: 1. Convert 100 watts into horsepower
LEFT: 2. How many cm are in 12 miles?
RIGHT: 2. How many cm are in 20 miles