Download Measurement and Significant Figures Mini Lab

August 3-4, 2011
Brain Teaser Quizlet
 Open Note Quizlet
 Place Notes (Ch 2.6-2.8) on your desk
Brain Teaser
 What do you think will happen if I light the
bubbles on fire?
 Why?
 Demo
 Record Observations
 Was your prediction correct?
 Explain the science behind it
Agenda
 Brain Teaser Quizlet
 Measurement Terms
 Numbers Notes:
 SI Units
 Intro to Significant Figures
 Measurement and Significant Figures Mini Lab
 Scientific Notation
 Homework
 Significant Figures Worksheet
 Qualitative and Qunatitative Worksheet
 Blubbenbacher’s Foods Lab Report  Due This Friday
Data Terms
 Quantitative
Measurements
Give results in a definite form,
usually values
 Examples
24L, 10 cm, 14 ºC
Data Terms
 Qualitative
Measurements
 Examples
Give results in a descriptive,
non-numeric form.
The beaker was warm.
The density was greater than
that of water.
Data Terms
 Accuracy
 Examples
How close a measurement comes
to the actual value of whatever
is being measured
Water freezes at 0º C, and boils at
100º C. How close is the
measurement to the values.
Data Terms
 Precision
Reproducibility of the measurement
 Examples
9 out of 10 lab groups report the
temperature of boiling water to be
95º C.
A basketball player shoots 20 free
throws, 18 of which bounce off the
right side of the rim.
Accuracy vs. Precision
 Target Practice
 Accurate
Precise
Accurate
& Precise
Percent error
Theoretical – Experimental x 100 = % error
Theoretical
Closure
 Give and example of a qualitative and quantitative
measurement.
Units of measurement
SI Units (Le Systéme Internationale)
 Scientists need to report data that can be
reproduced by other scientists. They need
standard units of measurement.
Base Units
• A base unit is a defined unit in a system of
measurement
•There are seven base units in SI.
Refer to the handout on SI Units
Base Units
Significant Figures
 Significant
Figures
Digits in a measurement that have
meaning relative to the
equipment being used
Significant Figures
 Place
What is the increment on the
equipment?
What you know for sure.
Significant Figures
 Digits with
meaning
Examples
Digits that can be known precisely
plus a last digit that must be
estimated.
Refer to Examples on the board:
1.
2.
3.
4
Scale Reading and Uncertainty
 Uncertainty: Limit of precision of the reading (based on
ability to guess the final digit).
 Existed in measured quantities versus counted quantities
 Refer to Example (2 rulers)
Significant Figures: Mini Lab
Equipment to Evaluate
 To what place (tenths,
hundredths, etc.) can
these measurement
instruments accurately
measure? What place is
the estimation?







Triple beam balance
Analytical balance
Thermometer
Graduated cylinders
Beakers
Ruler
Burette
Significant Figures
 What do you
notice?
Depends on type of equipment
being used.
Depends on size of equipment
used.
Significant Figures
 Raw Data Rules
 How do you know
how many sig figs?
1.
2.
3.
4.
5.
All digits 1-9 are significant.
Zeros between significant digits
are always significant.
Trailing 0’s are significant only if
the number contains a decimal
point
Zeros in the beginning of a
number with a decimal point are
not significant.
Zeros following a significant
number with a decimal are
significant.
Significant Figures
 Pacific to Atlantic Pacific = Decimal Present
Rule
 Examples
Start from the Pacific (left hand
side), every digit beginning
with the first 1-9 integer is
significant
20.0 = 3 sig digits
0.00320400 = 6 sig digits
1000. = 4 sig digits
Significant Figures
 Atlantic Rule to
Pacific
 Examples
Atlantic = Decimal Absent
Start from the Atlantic (right
hand side), every digit
beginning with the first 1-9
integer is significant
100020 = 5 sig digits
1000 = 1 sig digits
Practice

1.
2.
3.
4.
How many significant figures are in
400.0
4000
4004
0.004
Rally Rows
How many significant figures are in
1.
0.02
2. 0.020
3. 501
4. 501.0
5. 5000
6. 5000.
7. 5050
8. 01.0050
9. 50300
10. 5.0300
Summary
Things to consider
 What do significant figures tell you about the measurement
equipment?
 If you wanted to measure the mass of a whale, what scale
would you want to use? Would it matter if you know its
mass accurately to 1 gram?
 If you wanted to measure the mass a grain of sand , what
scale would you want to use? Would it matter if you know
its mass accurately to 1 gram?
Instrument Measure
 Need to make sure you are measuring and
recording to the correct number of digits
 Measure what you know for sure and then guess one
more digit
 Rulers
 Draw a line on your paper and measure it to the
correct number of digits
 Beaker vs. graduated cylinder
 Electronic balance vs. triple beam balance
Scientific Notation
 Scientific
Notation
 Example
Shorthand way of expressing
numbers that make them easier
to work with
6.02 x 1023
2.34 x 105
3.78 x 10-3
Scientific Notation
 Any Patterns?
Scientific Notation
 Rules
Base number 1-9
2. Exponent = the number of
times the decimal must be
moved to bring the base
number to 1-9.
3. Numbers greater than 1 have a
positive exponent, numbers
less than 1 a negative exponent
1.
Scientific Notation
 Examples
0.0025
2.5 x 10-3
1,750,000
1.75 x 106
Scientific Notation
 Problems
0.0000678
Express in
Scientific
Notation
998953000000
0.5768
Scientific Notation
 Problems
1.567 x 10-3
Express in
Standard
Notation
6.02 x 1023
3.14 x 102
Sig Figs in Scientific Notation
 The numbers expressed in the scientific notation
are significant
 Examples:
5.02 x 104  5.02 x 104  3 S.F
 The number of significant figures in a set of
numbers will be the # of sig figs in the scientific
notation.
 Examples:
50.200  5 SF  5.0200 x 101
Survivor Science


Convert the following to exponential notation or
to ordinary notation
Tell me how many Sig Figs.
1.
2.
3.
4.
5.
76
896745
8.9 x 103
3.45 x 10-1
0.222
6. 5.38 x 10-3
7. 5 million
8. 8.00 x 104
9. 0.00859
10. 953.6
Significant Figures in Calculations
 What are
Significant
Digits?
 Examples
 Triple Beam
Balance
 Graduated
Cylinder
 All the certain digits plus the
estimated digit in a measurement.
 How many decimal places can we
count
Significant Figures in Calculations
 Exact Numbers  Do not affect the number of
significant digits in the final answer.
They are not measurements!!
 Examples
 Infinite # of
sig figs
 1000m = 1 km
 12 in = 1 foot
Significant Figures in Calculations
 Multiplication
and Division
 The number with the smallest
number of significant digits
determines how many significant
digits are allowed in the final
answer.
 Example
 Volume of a box
 LxWxH
 (3.05m)(2.10m)(0.75m)
 2 sig figs
 4.8m3
Significant Figures in Calculations
 Example
 Density of a
penny
 M = 2.53g
V = 0.3mL
 D=M/V
 # significant figures allowed
 D = 8g/mL
Significant Figures in Calculations
 Addition and
Subtraction
 Example
 The number of significant digits
depends on the number with the
largest uncertainty. (you may be
using different scales)
Shoes
951.0 g
Clothes 1407
g
Ring
23.911 g
Glasses 158.18 g
Total
2540.
g
Significant Figures in Calculations
 Example
 What is the mass of a penny if,
the weighing paper alone has a
mass 0.67 g and weighing paper
plus the penny has a mass of 3.2
g.
3.2 g
-0.67 g
2.5 g
Significant Figures in Calculations
 Remember
A calculated number can only be as
precise as the least precise
measurement in the calculation.
Practice
Calculate each of the following to the correct number of
significant figures. Include units on your answer.
1. (25 g/mol)(4.0 mol) =
2. (3.48 in)(1.28 in)(0.010 in) =
3. 2.06 cm + 1.8 cm + 0.004 cm =
4. If the mass of a lead cube is 176.91 g and it measures 2.51cm
x 2.49 cm x 2.49 cm, what is the density of lead?
Practice
Calculate each of the following to the correct number of
significant figures. Include units on your answer.
1. (25 g/mol)(4.0 mol) =1.0 x 102
2. (3.48 in)(1.28 in)(0.010 in) = .045 in3
3. 2.06 cm + 1.8 cm + 0.004 cm = 3.9 cm
4. If the mass of a lead cube is 176.91 g and it measures 2.51cm
x 2.49 cm x 2.49 cm, what is the density of lead? 11.3 g/cm3
Rally rows
Sig figs in Calculations
1.
2.
3.
4.
5.
12 cm + 0.031cm + 7.969 cm =
(41.025 g - 23.38g) ÷ 8.01 mL=
17.3 cm x 6.2 cm + 3.28 cm2 =
109.3758 m2  45.813 m =
What is the mass of Salt (NaCl) if the sodium has a
mass of 22.99 g and the Cl a mass of 35.5g?
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