Conceptual Physics
Day 41 Tuesday January 6, 2015
Hello! Welcome back to Nerinx!!
Hope you all had a good Christmas! Hope you …
 Had some relaxation time
 Got Some sleep
 Some fun
 Received at least one really good gift
 had the satisfaction of giving someone a gift that she or he really liked
semester 1 final exam
15
2014 SEMESTER 1 FINAL EXAM
 HIGH SCORE: 100%
 MEAN SCORE: 80%
A
B
C
D
F
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 Good results overall!
 Be especially proud if your score % is improved compared with quarter test scores!!!!
 Some students did poorly on the final. I have suggestions on how you can do better 2nd
semester, and I will be contacting you.
Sr. Eileen/Mr. Balfe is going to hand these back now.
BUT before s/he does:
Put away all pencils, pens and markers. No pencils, pens or markers should be on the desks.
DO NOT WRITE ON THESE FINAL EXAMS!!
I keep the final exams as an example of your work, and I want them to show only what
you wrote during the exam.
You have 10 minutes to accomplish these tasks:
 First calculate your exam score. There are 200 possible points.
To get your score on the exam, multiply your scantron score by 4.
To get your percent, divide your score by 200, and then multiply by 100.
 Then check that your score in PowerSchool is correct.
 Then look at the exam questions you missed to see if they were graded correctly. If you
find what you think is an error in grading, write me a message on a separate piece of paper,
put your name on the paper and turn that paper in.
 Finally turn the exams back in.
Sister Eileen/Mr. Balfe: Please hand out exams and scantrons.
Turn them back in!!!!!! Sister Eileen/Mr. Balfe: Please count to make sure you have all
of them back.
If you want more time to look at your final exam, email me and we will set up a time
when you can do that.
TEACHER ANNOUNCEMENTS AND COMMENTS
Read these announcements:
5 minutes
Congratulations to our Quarter 2 Physics Phenoms:
A: Anna Pendleton
F: Kennedy Morganfield
G: Kassidy Grant
H: Sloane Montgomery
Topics for this semester
Unit 5
significant digits, momentum and energy
Unit 6
atoms, the electric force and electricity
Unit 7
electric circuits
Unit 8
waves and light
SNOW DAY POLICY
Sad to say, but snow days are not days off from Conceptual Physics class. I will contact
you via email and send you the lesson and the homework. You will study the lesson and
then do the daily homework, just as if you were in school. I will be available via email to
answer questions. This means you must always be aware of the weather, and if there is a
chance school will be called off, you must take home your physics binder, so that you will
be prepared to do the new lesson from home.
Get your planner out and write down the following important dates:
Quiz 5: Significant digits, unit conversions, momentum and energy
Day 49
A block
Wednesday
1/28/15
F G H blocks
Thursday
1/29/15
IH5 and IH6
Your first IH email is due to Dr. Leopold on day 50
A block
before the start of Conceptual Physics class on Friday
F G H blocks
before the start of Conceptual Physics class on Monday
1/30/15
2/2/15
Your second IH email is due to Dr. Leopold on day 61
A block
before the start of Conceptual Physics class on Thursday
3/5/15
F G H blocks
before the start of Conceptual Physics class on Friday
3/6/15
The descriptions of, and directions for, IH5 and IH6 are posted on our course website.
Significant digits
Today’s new material:
I. Significant digits rules for measured numbers
II. Significant digits of exact numbers
III. Significant digits rules when multiplying and dividing
45
As you are working on this lesson, feel free to ask Sr. Eileen for help. You may also
email me you questions.
I. Significant digits rules for measured numbers - 20 min
A. If a number is measured, then it is an approximate number and it has
significant digits.
Example: Say that we measure the mass of some object using a triple beam balance.
We write our answer as:
m = 543.22 grams
because, as you recall, we can read to mass to the nearest one hundredth of a gram using
our balances.
The last digit on the right is an estimate.
We are telling people who read our measure value of mass that we know 5 digits and we
don’t know anymore. The mass of the object could be 543.221 grams or 543.224 grams
- we just don’t know. We are also saying that when someone else measures the mass of
this object, with same equipment we used, we expect her to get the same answer we got:
543.22 grams, or perhaps 543.21 grams or 543.23 grams.
But nothing more different than that.
We say, “This quantity has 5 significant digits (significant figures).”
The number of significant digits a quantity has remains the same regardless of whether
the write the quantity in standard notation, or in scientific notation. So if we write the
mass above in scientific notation:
m = 5.4322 x 102 grams
we see that it still has 5 significant digits.
Note: significant digits are different than decimal places!
B. Any non-zero digit counts as a significant digit.
Somebody made the following measurements. How many significant digits (figures) are there
in each of these measured quantities?
1. 543 kg
=
5.43 x102 kg
Answer: 3 significant digits
0
2. 1.45 m
=
1.45 x 10 m
Answer: 3
6
3. 2,456,733 N =
2.456733 x 10 N
Answer: 7
Again, be sure you realize that significant digits are NOT the same as decimal places.
C. Any zero between non-zero digits (any zero not at the beginning or end) counts as a
significant digit
Somebody made the following measurements. How many significant digits (figures) are there
in each of these measured quantities?
4. 1045
s
=
1.045 x 103 s
Answer: 4 significant digits
1
5. 10.045 N
=
1.0045 x 10 N
Answer: 5
5
6. 650,002 m/s =
6.50002 x 10 m/s
Answer: 6
OK, this is pretty clear. However, pay attention now. Things are going to get tricky.
D. For numbers written without a decimal point, zeros on the right (at the far right end)
are NOT significant – they are just place-holders. And there are never any zeros on the
left (at the far left end) for numbers without a decimal point.
Somebody made the following measurements. How many significant digits (figures) are there
in each of these measured quantities?
7. 2,000,000,000 mi =
2 x 109
mi
Answer: 1 significant digit
3
8. 1450 hr
=
1.45 x 10 hr
Answer: 3
E. For numbers written with decimal point, zeros on the right (at the far right end) ARE
significant; but zeros on the left (at the far left end) are not significant.
Somebody made the following measurements. How many significant digits (figures) are there
in each of these measured quantities?
9. 1.4500 ft
=
1.4500 x100 ft
Answer: 5 significant digits
Both of the two zeros at the far right end are significant digits.
10. 0.00145 m =
1.45 x 10-3 m
Answer: 3 significant digits
None of the three zeros at the far left end are significant digits
NOTE TO SELF: need this type of example (#10) so they don’t think only zeros to left of
decimal aren’t sig
Do you need some more practice? Make up a number or two, and then try to figure out how
many significant digits it has. Work as a group at your table. Be quick. You only have 5
minutes for this.
II. Significant digits of exact numbers – 5 minutes
Some numbers are EXACT NUMBERS. Counting numbers, like 5 apples or 2 cars, are exact
numbers.
If you are told a number is exact, then it is an integer AND you are to think of that number as
having an infinite number of significant digits.
o 7 days (exact) means 7.000000000…. with 0 repeating forever!
o 60 seconds (exact) means 60.0000000…. with 0 repeating forever!
It is not always immediately clear whether a number is exact or not. You have to think about
it. And you can ask your teacher when you are not sure. For instance, when we say, “There
are 7 days in a week.”, the 7 is an exact number, because our week is defined to last exactly 7
days long. So the 7 is exact, and has an infinite number of significant digits. But when we
say, “She was sick for 7 days,” the 7 is a measured number – an estimate - with 1 significant
digit. She was sick for ABOUT 7 days. Maybe she was sick for 6 days and 23 hours, or
maybe she was sick for 7 days and 3 hours. We don’t know exactly.
III. Significant digits rules when multiplying and dividing – 5 minutes
The answer to any MULTIPLICATION OR DIVISION problem (including conversion
problems) has only as many significant digits as the input number with the least number of
significant digits.
How many significant digits should you give for each of these?
vx = (9.81 m/s2) (4.763 s)
Answer: 3 significant digits
m
s
ax 
6.44589 s
2.3
Answer: 2
Answer has only as many sig fig as the input number with the least number of sig dig

Now, remember that exact numbers have an infinite number of significant digits – so exact
numbers never limit the number of significant digits in the answer.
In the example below, 7 is an exact number:
How many significant digits should you give for each of these?
(45 weeks) (7 days/week)
Answer: 2
Note that 45 has 2 significant digits, and 7 days/week has an infinite number of significant
digits – so the 45 has the smaller number of significant digits.
II. Unit conversions - getting sig fig correct – 10 minutes
Sr. Eileen/Mr. Balfe: please HAND OUT CONVERSION SHEETS, one per student.
A familiar example
Convert 25 miles/hour into m/s, AND get number of significant digits right.
25 miles 1609 m
1h
m


 11
1h
1mile
3600 s
s

Your calculator will show 11.1736111, but you have to know that only two of these digits are
significant. The way you know is: The 1 h, the 1 mile, and the 3600 s are all exact numbers
with an infinite number of significant digits. It says this on your conversion sheet. The 1609
m has four significant digits. The 25 miles has two significant digits. So the quantity with the
smallest number of significant digits is the 25 miles and it has 2 significant digits. Therefore
the answer to the calculation has two significant digits.
IMPORTANT: IN ALL CALCULATIONS, KEEP ALL DIGITS TILL THE END, AND
ONLY THEN ROUND TO THE CORRECT NUMBER OF SIGNIFICANT DIGITS.
Sr. Eileen/Mr. Balfe: Please hand out daily homework sheets
What is my daily homework today?
DH 27 – Significant Figures, Scientific Notation, and Unit Conversions
5 minutes
1. You must complete questions 1 – 9 and 12-14, no matter how long it takes you.
2. You also must work a minimum of 45 minutes on the homework.
So if you finish 1 – 9 and 12-14, and you have not yet spent 45 minutes, you must go back
and do 10 and 11. You may stop after 45 minutes of work, even if you have not finished 10
and 11.