Transcript sig figs - USD305.com

Unit 2
Chapter 3
Scientific Measurement
Today…



Turn in:
 Nothing
Our Plan:
 Daily Challenge
 Scientific Notation, Accuracy, Precision, Error Notes
 Worksheet #1
 Wrap Up – Rally Robin
Homework (Write in Planner):
 Complete WS #1 by next class
Daily Challenge

The number
602200000000000000000000 is
used so frequently in chemistry
that it has its own name;
Avogadro’s number. What
would be a better way of
writing it?
Scientific Notation

1.
2.
3.
To write a number in
scientific notation:
Move the decimal so that the number is
between 1 and 10.
The exponent is the number of tens places
you moved the decimal
Moving the decimal right = - exponent
Moving the decimal left = + exponent
Examples
65000 m = 6.5 x 104 m
 0.0000156 s = 1.56 x 10-5 s
-1
 0.24 m/s = 2.4 x 10 m/s
 6.7 mm = 6.7 x 100 mm

To Write a number in
Standard Form
Change it from scientific notation
to a standard number by moving
the decimal.
 Example
1.4 x 106 = 1,400,000
2.6 x 10-4 = 0.00026

Adding & Subtracting
Change the numbers to the same
exponent.
 Add or subtract the numbers

Example: 4.1 x 106 + 8.5 x 107
 0.41 x 107 + 8.5 x 107 = 8.91 x 107

Multiplication
Multiply the numbers
 Add the exponents

Example: (4 x 106)(2 x 108)
 8 x 1014

Division
Divide the numbers
 Subtract the exponents

Example: (9 x 107)/(3 x 104)
 3 x 103

Try It Out!
1.
2.
3.
4
10
5
10
3.5 x
+ 5.1 x
(5.7 x 108)(3.5 x 106)
6
3
(6.9 x 10 )/(4.5 x 10 )
Answers
1.
2.
3.
5
10
5.45 x
15
1.995 x 10
3
1.53 x 10
Or…
Use your scientific calculator.
 The EE button means x10^
 Do the Try it Out problems
again using your calculator and
see if you get the correct
answers!

Accuracy & Precision
Accuracy – compare to the
CORRECT value
 Precision – compare to the
values of two or more
REPEATED MEASUREMENTS

Accurate, Precise, Both, Neither?
Accurate
Accurate, Precise, Both, Neither?
Precise
Accurate, Precise, Both, Neither?
Neither
Accurate, Precise, Both, Neither?
Precise
Accurate, Precise, Both, Neither?
Both
Accurate, Precise, Both, Neither?
Accurate
Percent Error
Percent Error = |experimental - actual|
X 100
actual value

The absolute value is present so that percent
error is always POSITIVE!
Example

Working in the laboratory, a student finds the
density of a piece of pure aluminum to be 2.85
g/cm3. The accepted value for the density of
aluminum is 2.699 g/cm3. What is the student's
percent error?
Percent Error = |2.85 – 2.699|
X 100 =
2.699
5.59%
Try It Out

A student takes an object with an accepted mass
of 200.00 grams and masses it on his own
balance. He records the mass of the object as
196.5 g. What is his percent error?
Percent Error = |196.5 – 200.00|
X 100 =
200.00
1.75%
STOP!
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
Complete Worksheet #1 by next
class
Worksheets are…
A completion grade (i.e. You do not
get a grade until it is 100% finished)
 10 points on time
 -2.5 points each day it’s late

Wrap Up

Rally Robin
Pair up with your shoulder partner.
Divide a deck of cards in half. Take
turns asking each other the questions
on the cards.
 Be sure to cover the answer with
your finger.

Today…
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

Turn in:
 Get out WS#1 to Check
Our Plan:
 Scientific Notation Clicker Review
 Scientific Notation Quiz
 Notes – Significant Figures/Units of Measurement
 WS #2
 Bluff
Homework (Write in Planner):
 Complete WS #2 by next class (9/12)
 QUIZ OVER SIG FIGS NEXT TIME!
Units in Chemistry
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When you add or subtract two numbers, they must have the
same units.
The answer then has those units as well.
Example: 4 m + 12 m = 16 m
When you multiply, you also multiply the units.
Examples:


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
4 m x 5 m = 20 m2
2 g x 3 s = 6g·s
When you divide, you also divide the units.
Examples:


4 m / 2 s = 2 m/s
8 g / 2 mL = 4g/mL
Challenge!

What does the word
“significant” mean?
Significant Figures

The numbers that are
known, plus a digit that
is estimated
RULES
***All nonzero numbers are significant***
125, 689 has 6 significant figures (sig figs)
156 has 3 sig figs
1.
Zeros between nonzero
numbers are significant.

3
40.7 mL has ______
sig figs

6 sig figs
870,009 g has _____
RULES
2.
Zeros in front of nonzero
numbers are not
significant

2 sig figs
0.00011 s has _____

3 sig figs
0.956 g/mL has _____
RULES

Zeros at the end of a number
and to the right of a decimal
are significant
6 sig figs
85.0000 kg has _____

9 sig figs
2.00000000 L has _____
3.
RULES
4.
Zeros at the end of a number
are NOT significant. If there
is a decimal at the end, they
ARE.

4 sig figs
2000. m/s has _____

1 sig figs
2000 m/s has _____
EASY RULE!
Decimal Start at the first nonzero
number on the left and
count every number right
No
Start at the first nonzero
Decimal number on the right and
count every number left
Unlimited Significant Figures

Counting – There are 23 students in the
classroom


Could also be expressed as 23.0 or
23.00000000000000 etc.
Conversion Factors – 60 min = 1 hour

Exact quantities do not affect the process of
rounding
Try It Out

1.
2.
3.
4.
5.
6.
How many sig figs?
0.00125 3
1.12598000 9
3,000 1
0.0100103 6
5,500. 4
1.23 x 105 3
Rounding

1.
2.
3.
4.
Round the following numbers so
that they have 3 significant figures:
1.36579 = 1.37
120 = 1.20 x 102 OR 120.
145,256,987 = 145,000,000
0.0001489651 = 0.000149
To Multiply & Divide
Sig Figs…
1.
2.
Count the number of sig figs
in each number
Round the answer so that it
has the same number of sig
figs as the number in the
problem with the fewest.
Example 1



16.19 g / 4.2 mL
= 3.8547619 g/mL
16.19 has 4 sig figs
4.2 has 2 sig figs, so the answer should
have 2 sig figs
3.9 g/mL
Example 2
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
9.3 m x 0.00167 m
= 0.015531m2
9.3 m has 2 sig figs, 0.00167 has 3 sig figs
Therefore, the answer must have only 2
sig figs.
0.016 m2
Try It Out!
(1.23)(0.011) = 0.014
 12.63000/100 = 0.1


(1.23 x 106)(3.5 x 104) = 4.3 x 1010

0.0045912/6.570 =
6.988 x 10-4
Stop

Complete Worksheet #2
Bluff
1A. How many sig figs are in 0.001023?
1B. Solve 456 x 3.2
2A. How many sig figs would the answer have
if you calculated 2.1 x 0.01?
2B. How many sig figs are in 123,000?
3A. Solve 2.7 x 3
3B. How many sig figs would the answer have
if you calculated 1.4/3.789?
Bluff
4A.
4B.
5A.
5B.
6A.
6B.
What is 235,489 rounded to 2 sig figs?
Solve 1/236
Solve 3.7914/9.2
What is 1,926,560 rounded to 1 sig fig?
How could you write 230 with 3 sig figs?
What is 0.00056798 rounded to 4 sig figs?
Today…
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

Turn in:
 Get out WS#2 to Check
Our Plan:
 Sig Fig Race
 Sig Fig Quiz
 Notes – Significant Figures in Measurement
 Practical Lab - Measurement
 Wrap Up – Measure Up
Homework (Write in Planner):
 Fill out p. 9 – top of 11 using your text by next class!
Sig Figs in
Measurements
When doing any measurements in
chemistry, it is important that you
use the correct precision.
 All measurements should be
made by writing all units you
know and estimating the last unit.

Examples
10
20
30
40
54
50
70
60
38
10
30
20
50
40
70
60
13.9
2
4
6
8
10
12
14
More Examples!
2
4
6
0.5
1
1.5
20
40
60
3.4
1.16
72
Units of Measurement
Every measurement in
chemistry MUST HAVE A
UNIT!
 Without a unit, the number
means nothing!
 We will use SI units in class

Wrap Up – Clicker!
2
4
5
6
0.5
1
1.5
20
40
60
5.3
1.58
43
Today
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

Before Class:
 Get out Note Booklet, Calculator, & Pencil
Our Plan:
 Mix/Group Review (#1-11)
 Challenge
 Notes - Conversions
 WS #3
 Wrap Up – Practice Problem from the Worksheet
Homework (Write in Planner):
 Try out some of the problems on the worksheet
Review Time


Open up your notebooklet to p. 11.
Answer questions 1 – 6.
Get up and move around the classroom.
When the instructor says “group by the
answer to #___” you have to form a
group of students that is the same as
the answer to the problem!
Review Time
Now answer questions 7 – 11
on your own.
 When you are finished pair up
with your face partner and
share your answers.

Mix/Group
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How many sig figs:
1. 102.32500
2. 560.
3. 0.0012501
What is the exponent?:
4. 420=
5. 36,000,000
6. 60 =
Think-Pair-Share

Round these numbers so that they have 3 sig figs:
7.
8.
9.
10.
11.
103,250 103,000 or 1.03 x 105
567.9 568 or 5.68 x 102
0.0012561 0.00126 or 1.26 x 10-3
100
100. or 1.00 x 102
Read the measurement below correctly.
20
40
60
43
Challenge
Would you be breaking the
speed limit in a 40 mi/h zone
if you were traveling at 60
km/h?
 http://www.youtube.com/wat
ch?v=Qhm7-LEBznk

Challenge

How old are you, in
minutes?
Conversion Factors
Definition: a ratio of equivalent
units
 It is always equal to 1
 When multiplying by a conversion
factor, the numerical value is
changed, but the actual size of the
quantity remains the same

Conversion Factors
When working with conversion
factors, we use the Factor-Label
Method (dimensional analysis)
 The factor is the number that
explains the relationship between
two things
 The labels are its’ units

Examples

4 quarters = 1 OR
1 dollar
Factor
1 dollar = 1
4 quarters
Label
Examples
12 months = 1
1 year
1 foot
12 inches
=1
Rules for using Conversion
Factors
1.
2.
3.
Always start by writing what you
know from the problem.
Multiply by a conversion factor so
that the units cancel out (same unit
in numerator and denominator)
Continue converting until your answer
is in the desired units.
Example 1 – your age in
minutes
Checklist:
I started by writing what I knew
All units cancel
My answer is in minutes
Mrs. C’s top 4 reasons for NOT
using the Factor-Label Method
1.
2.
You’re super-intelligent and
enjoy solving relatively
simple problems in the
most complex manner.
You're tired of always
getting the correct
answers.
Mrs. C’s top 4 reasons for NOT
using the Factor-Label Method
3.
You’re artistic, and rather than
using Mrs. C’s concretesequential method of solving
problems you want to use your
own random method such that
you create abstract patterns and
designs on paper that you might
be able to sell as artwork.
Mrs. C’s top 4 reasons for NOT
using the Factor-Label Method
4.
Let's say that you have no
interest in going to the prom or
making the soccer team, and you
don't mind being unpopular,
unattractive, ignorant, insecure,
uninformed, and unpleasant.
Otherwise,
You Need the Factor-Label Method!
Testimonials

"I was a South High School student who dozed off
while Mrs. C taught us the Factor-Label method in
chemistry. I never quite got the hang of it. It irritated
me... all of those fractions. I never really liked
fractions. Although my grades had been pretty high, I
got a D in chemistry and subsequently did not take
any more high school science classes. It was not long
before I started on drugs, and then used crime to
support my drug habit. I have recently learned the
factor-label method and realize how simply it could
have solved all of my problems. Alas, it is too late. I
won't get out of prison until 2022 and even then, my
self image is permanently damaged. I attribute all of
my problems to my unwillingness to learn the factorlabel method." -Jane
Testimonials

"I thought I knew everything and that sports was the only
thing that mattered in high school. When Mrs. C taught our
class the factor-label method, I didn't care about it at all. I
was making plans for the weekend with my girlfriend who
loved me because I was a running back and not because of
chemistry. While other kids were home solving conversion
problems, I was practicing making end sweeps. Then one
day I was hit hard. Splat. My knee was gone. I was a total
loser. My girl friend deserted me. My parents, who used to
brag about my football stats, stopped loving me and started
getting on my case about grades. I decided to throw myself
into my school work. But I couldn't understand anything. I
would get wrong answers all of the time. I now realize that
my failure in school came from never having learned the
factor-label method. I thought everyone else was smarter
than me. After the constant humiliation of failing I finally
gave up. I am worthless. I have no friends, no skills, no
interests. I have now learned the factor-label method, but it
is too late." -Bill
Example 2

How many dollars do you have if you
have 38 quarters?
9.5 dollars
Example 3

How many nanoseconds are in one week?
600,000,000,000,000
nanoseconds
Example 4

How many milligrams are in 12 g?
12,000 mg
TRY IT OUT!

Now try the next three
problems in your notes on
your own.
Checklist:
I started by writing what I knew
All units cancel
My answer is in desired units
The Answers…
1.
2.
3.
790,000,000 seconds
3
6.71 x 10 grams
3
5.3 x 10 mL
STOP!
Start Worksheet #3.
 You must show work and
you must use the factorlabel method!

Today…

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
Turn in:

Get WS #3 out

On Mrs. C’s birthday she will be 1.041 x 109 seconds old. How many years
old will she be?
Our Plan:

Pass the Paper

Work on Worksheet #3

Notes - Density

WS #4

Wrap Up – Density Problem
Homework (Write in Planner):

Complete WS #3 &#4 by next class

QUIZ OVER BOTH WORKSHEETS NEXT TIME!
Review

Pass the Problem


Each student has a problem to solve. The
first student will do step 1 (write what you
know) and pass the paper to the next
student who will complete the second step.
Continue passing the paper until you get
the answer.
Example: How many days are in 60
seconds?
Pass the Paper Answers
569
96,400
8
1,000,000

Density Review
Density = Mass/Volume
 Volume of liquids is measured
in liters or milliliters
 Volume of solids is length x
width x height

Example


A bar of silver has a mass of 68.0
g and a volume of 6.48 cm3.
What is the density of silver?
10.5 g/cm3
Example


A copper penny has a mass of 3.1
g and the density of copper is
8.8571 g/cm3. What is the
volume of the penny?
0.35 cm3
Try It Out


What is the mass of a pure silver
coin that has a volume of 1.3
cm3? The density of silver is 10.5
g/cm3.
14 g
STOP!
Complete
Worksheet #4

Wrap Up - Density Review (p. 15 Notes)
• Four graduated cylinders each contain a
different liquid: A, B, C, and D.
• Liquid A: mass = 18.5 g; volume = 15.0 mL
• Liquid B: mass = 16.5 g; volume = 8.0 mL
• Liquid C: mass = 12.8 g; volume = 10.0 mL
• Liquid D: mass = 20.5 g; volume = 12.0 mL
• Examine the information given for each liquid,
calculate the density, and predict the layering of
the liquids if they were carefully poured into a
larger graduated cylinder.
Density Review
A – 1.23 g/mL
C – 1.28 g/mL
D – 1.71 g/mL
B – 2.1 g/mL
Density = Mass/Volume
Today…



Turn in:
 Get WS #3 & #4 out to be graded
Our Plan:
 Which Word Am I?
 Conversions/Density Quiz
 Lab
 Wrap Up – High Five
Homework (Write in Planner):
 Missing Work
Review – Which Word Am I
(p. 15 Notes)
1.
2.
3.
4.
5.
6.
Mass divided by volume
The numbers that are known in a measurement
plus one estimated digit
How close your measurements are to the true
value
How close your measurements are to each other
Convert 3.69 meters into inches.
What is the volume of a cube that has a mass of
7.9 g and a density of 9.45 g/cm3?
Wrap Up

What questions do you
have on the lab?
Today…


Turn in:
 Get Lab Packet Out, Calculator, Pencil
Our Plan:
 LAB – DUE TODAY
 Work Day



Missing Work
Test Review
Homework (Write in Planner):
 Test Review due next class
 TEST NEXT TIME!
Today…



Turn in:
 Get out Test Review to check
 Turn in Measurement Lab if you haven’t yet!
Our Plan:
 Worksheet Race
 Go over Test Review, then turn it in
 Unit 3 Test
 Periodic Table Basics Activity
Homework (Write in Planner):
 PT BASICS DUE NEXT MONDAY!
After the Test

PT BASICS HELP