Transcript Chapter 3 Scientific Measurement

Chapter 3
Scientific Measurement
Hingham High School
Mr. Clune
Measurements


Qualitative measurements - words
Quantitative measurements –
involves numbers (quantities)



Depends on reliability of instrument
Depends on care with which it is read
Scientific Notation
 Coefficient raised to power of 10
Scientific Notation

Multiplication
 Multiply the coefficients, add the
exponents
4+7=
(2 X
2X3=6
4
10 )
X (3 X
11
7
10 )
6X
11
10
Scientific Notation

Division

Divide the coefficients, subtract
the denominator exponent from
numerator exponent
9
8 X 10
8
=2
4
4X
5
10
9-5=4
2X
4
10
Scientific Notation


Before adding or subtracting in
scientific notation, the exponents
must be the same
Calculators will take care of this
Scientific Notation

Addition
 Line up decimal; add as usual the
coefficients; exponent stays the same
4
10 )
6
10 )
(25 X
+ (3.0 X
4
4
(25 X 10 ) + (300. X 10 )
(325 X
4
10 )
Scientific Notation

Subtraction
 Line up decimal; subtract coefficients as
usual; exponent remains the same
4
10 )
3
10 )
(25 X
- (150. X
4
4
(25 X 10 ) - (15.0 X 10 )
(10 X
4
10 )
Measurements and
Their Uncertainty



Need to make reliable
measurements in the lab
Accuracy – how close a
measurement is to the true value
Precision – how close the
measurements are to each other
(reproducibility)
Bad Accuracy
And
Good Precision
Bad Accuracy
And
Bad Precision
Good Accuracy
And
Bad Precision
Good Accuracy
And
Good Precision
Measurements and
Their Uncertainty



Accepted value – correct value based
on reliable references
Experimental value – the value
measured in the lab
Error – the difference between the
accepted and experimental values
Measurements and
Their Uncertainty


Error = accepted – experimental
 Can be positive or negative
Percent error = the absolute value
of the error divided by the
accepted value, times 100%
| error |
% error =
accepted value
x 100%
% Error Example
Accepted Value = 100g
Experimental Value = 102g
% Error =
| Acc – Exp |
X 100%
Acc
% Error =
| 100 – 102 |
X 100%
100
% Error = 2%
Significant Figures



Significant figures in a
measurement include all of the
digits that are known, plus a last
digit that is estimated.
Note Fig. 3.4, page 66
Rules for counting sig. figs.?
 Zeroes are the problem
 East Coast / West Coast method
Significant Figures
1. All nonzero digits
• 457 cm (3)
• 0.35 g (2)
2. Zeros between nonzero digits
• 10003 mL (5)
• 0.2005 ms (4)
Significant Figures
3. Zeros to the left of the first
nonzero digits in a number are
not significant; they merely
indicate the position of the
decimal point.
• 0.02 g (1)
• 0.0026 cm (2)
Significant Figures
4. When a number ends in zeros that
are to the right of the decimal
point, they are significant.
• 0.0200 g (3)
• 3.0 cm (2)
Significant Figures
5. When a number ends in zeros that
are not to the right of a decimal
point, the zeros are not necessarily
significant.
•130 cm (2)
•10,300 g (3)
Counting Significant Fig.



Sample 3-1, page 69
Rounding
 Decide how many sig. figs. Needed
 Round, counting from the left
 Less than 5? Drop it.
 5 or greater? Increase by 1
Sample 3-2, page 70
Sig. fig. calculations


Addition and Subtraction
 The answer should be rounded to
the same number of decimal places
as the least number in the problem
Sample 3-3, page 60
Sig. fig. calculations
this has the least
digits to the right of
the decimal point (2)
26.46
+ 4.123
30.583
{
Rounds off to
30.58
Sig. Fig. calculations


Multiplication and Division
 Round the answer to the same
number of significant figures as the
least number in the measurement
Sample 3-4, page 61
Sig. Fig. calculations
2.61
x1.2
3.132
this has the smaller
number of significant
figures (2)
{
Rounds off to
3.1
International System of Units



The number is only part of the
answer; it also need UNITS
Depends upon units that serve as a
reference standard
The standards of measurement used
in science are those of the Metric
System
International System of Units




Metric system is now revised as the
International System of Units (SI),
as of 1960
Simplicity and based on 10 or
multiples of 10
7 base units
Table 3.1, page 63
International System of Units


Sometimes, non-SI units are used
 Liter, Celsius, calorie
Some are derived units
 Made by joining other units
 Speed (miles/hour)
 Density (grams/mL)
Common prefixes






Kilo (k) = 1000 (one thousand)
Deci (d) = 1/10 (one tenth)
Centi (c) = 1/100 (one hundredth)
Milli (m) = 1/1000 (one thousandth)
Micro () = (one millionth)
Nano (n) = (one billionth)
Length


In SI, the basic unit of length is the
meter (m)
 Length is the distance between
two objects – measured with
ruler
We make use of prefixes for units
larger or smaller
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
Volume Measuring Instruments





Graduated cylinders
Pipet
Buret
Volumetric Flask
Syringe
Volume changes?



Volume of any solid, liquid, or
gas will change with
temperature
Much more prominent for
GASES
Therefore, measuring
instruments are calibrated for a
specific temperature, usually
20 oC, which is about normal
room temperature
Volume – (m3)
Volume (L)
3
1dm =1L
Volume
Volume (mL)
1cm
3
1cm =1mL
1cm
1cm
Volume – Liter (L)
Units of Mass


Mass is a measure of the
quantity of matter
 Weight is a force that
measures the pull by gravityit changes with location
Mass is constant, regardless of
location
Mass – KiloGram (kg)
Working with Mass


The SI unit of mass is the
kilogram (kg), even though a
more convenient unit is the
gram
Measuring instrument is the
balance scale
Temperature
 Kelvin
(K)
 Based on Absolute Zero
 Celsius (°C)
 Water freezes at 0°C (273K)
 Water boils at 100°C (373K)
Temperature
 Water
freezes at 0°C (273K)
 Water
boils at 100°C (373K)
Temperature (°C, K)
BP of H2O
FP of H2O
Absolute
Zero
Temperature
 Convert
Kelvin to Celsius
°C = K - 273
345K = ? °C
°C = 345K – 273
72°C
Temperature
 Convert
Celsius to Kelvin
K = °C + 273
20 °C = ? K
K= 20°C – 273
293K
Time – Seconds (s)
Energy
The capacity to do work
or produce heat
 Joule
(J)
 Calorie (Cal)
 Energy needed to raise 1g
of 1 °C
Homework
Practice Problem 16
Page 78
Section Assessment
Questions: 18-27(odd)
Page 79
Due: 10/7/04
Dimensional Analysis
Converting Units
Conversion Problems
50cm = ?m
100cm = 1m
100cm
1m
1m
100cm
Conversion Problems
1m
50cm X
=
100cm
0.50 m
Conversion Problems
0.045kg =? g
1000g = 1kg
1000g
1kg
1kg
1000g
Conversion Problems
1000g
0.045kg X
1kg
45g
=
Conversion Problems
2.5hr =? s
60min = 1hr
60min
1hr
1hr
60min
Conversion Problems
2.5hr =? s
60s = 1min
60s
1min
1min
60s
Conversion Problems
60s
60min
2.5hr X
X
min
1hr
9000s
=
Homework
Practice Problem 35-37
Pages 82 - 86
Due: 10/7/04
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
Density
The formula for density is:
mass
Density =
volume
• Common units are g/mL, or
3
possibly g/cm , (or g/L for
gas)
• Density is a physical property,
and does not depend upon

Things related to density



What happens when corn oil
and water are mixed?
Why?
Will lead float?
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
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?
Sample 3-10,11, page 91-92
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
 1g of H2O = 1mL = 1 g/cm3
Formula
Specific
gravity
=
3
(g/cm )
D of substance
D of water (g/cm3)
•
•
•
Note there are no units left, since
they cancel each other
Measured with a hydrometer – p.72
Uses? Tests urine, antifreeze, battery
Temperature



Heat moves from warmer object to
the cooler object
 Glass of iced tea gets colder?
Remember that most substances
expand with a temp. increase?
Basis for thermometers
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
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
Temperature scales





Water freezes at 273 K
Water boils at 373 K
0 K is called absolute zero, and
equals –273 oC
Fig. 3.19, page 75
Sample 3-6, page 75