Transcript PPt - My eCoach

Unit 2:SCIENTIFIC MEASUREMENT
OBJECTIVES
(Don’t Copy!)
 Convert Between Standard Notation to
Scientific Notation
 Identify Significant Figures & Uncertainty in
Measurements
 Perform Operations with Significant Figures
 Addition & Subtraction
 Multiplication & Division
NOTE: PLEASE COPY EXAMPLES IN THIS
SLIDESHOW
1
What is Scientific Notation?
 a way of expressing really big numbers or
really small numbers.
 For some numbers, scientific notation is
more concise.
2
Scientific notation consists of
two parts:
 A number between 1 and 10 (the
“coefficient”)
 A power of 10
 Ex:
7.01 x
8
10
3
Converting from
StandardScientific Notation
EX: Convert 289,800,000 to scientific notation.
8
2.898
___
_______ x 10
STEP 1: Moving the decimal, convert this number
so that it falls between 1 and 10.
STEP 2: Count the number of places you moved
the decimal. This is the exponent.
• If the number was large to start with, exponent is positive
• If the number was small to start with, exponent is negative
4
Examples
 Given: 0.000567
NOTE: This is a
very small number,
so the exponent is
SMALL (negative)
-4
___
5.67
___________ x 10
STEP 1
STEP 2
5
Converting Scientific
Notation to Standard
 Ex: 9.301 x 10 -7
STEP1 : Using the sign on the exponent, decide which
way to move your decimal.
• Negative sign, move to the left (negative direction)
• Positive sign, move to the right (positive direction)
STEP 2: Move the decimal the same number of spaces as the exponent
indicates.
Use zeros to hold “empty” spaces.
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Scientific Notation & Your
Calculator
 Video Instructions- Using Calculator
7
Plugging Scientific Notation
into My Calculator
 Find the button on your calculator that is used to
enter SCIENTIFIC NOTATION. Write it HERE___

EE
OR

EXP
 (Do Not Copy) Note: If you find one of the
symbols ABOVE a key, rather than ON a key, you
must push

2nd
EE
OR

2nd
EXP
8
Plugging Scientific Notation
Into My Calculator
 Ex: Plug this number into your calculator:
8.93 x 1o-13
 (leave the blanks empty for now)
 Write the steps you used below
1.
NOTE:
Sometimes
these 2
steps can
be
reversed
2.
3.
4.
5.
NOTE: Use your
Type 8.93
calculator’s keys
EE button.
if they differ from
Push ______
what is written
Type_____13_____
here
(-) button
+/Push ____OR____
8.93 -13
What I see on the screen is _________
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Scientific Notation: Doing Calculations
Ex: 3 x 104 + 2.5 x 105
Problem 3 x 104 + 2.5 x 105
USE
CALCULATOR:
NOTE: Use your
calculator’s keys if
they differ from
what is written in
table & fill them in
What you 3 EE 4
type
What you
see on
calculator
304
+ 2.5 EE 5
2.505
NOTE: Answers must be in scientific notation!
Calculator says: 280000
Correct Answer: 2.8 x 105
10
Practice
 9.1 x 10-3 + 4.3 x 10-2
Calculator says: 0.0521
ANSWER: 5.21 x 10-2
11
Scientific Notation:Multiplying&Dividing
Ex: (6.1 x 10-3) (7.2 x 109)
-3 x 7.2 x 109
Problem
6.1
x
10
USE
CALCULATOR: What you 6.1 EE 3- x 7.2 EE 9
NOTE: Use your
calculator’s keys
if they differ from
what is written in
table
type
What you
see on
calculator
6.1-03
7.209
NOTE: Answers must be in scientific
notation!
Calculator says: 43920000
Correct Answer: 4.392 x 107
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Stating a Measurement
In every measurement there is a
Number followed by a
 Unit from a measuring device
The number should also be as precise as the
measuring device.
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Ex: Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)= 2
Second digit (known)
cm
2.?? cm
= 0.7
2.7? cm
Third digit (estimated) between 0.05- 0.07
Length reported
=
2.75 cm
or
2.74 cm
or
2.76 cm
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Significant Figures
The numbers reported in a measurement
are limited by the measuring tool
Significant figures in a measurement
include the known digits plus one
estimated digit
15
Shortcuts to Sig Figs
The Atlantic-Pacific Rule says:
"If a decimal point is Present, ignore zeros on
the Pacific (left) side.
If the decimal point is Absent, ignore zeros on
the Atlantic (right) side.
Everything else is significant."
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Counting Significant Figures:
Unlimited Sig Figs
2 instances in which there are an unlimited # of sig
figs.
a) Counting. Ex: 23 people in our classroom.
b) Exactly defined quantities. Ex: 1hr = 60 min.
 Both are exact values. There is no uncertainty.
 Neither of these types of values affect the process
of rounding an answer.
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Learning Check (Do Not Copy)
A. Which answers contain 3 significant figures?
1) 0.4760 2) 0.00476 3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300 3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
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Learning Check (Do not copy)
In which set(s) do both numbers contain
the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
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Rounding
With
Sig
Figs
 When rounding an answer, determine which is
the last significant figure. This is where you will
round your number.
 If the digit immediately to the right of the last sig
fig is less than 5, the value of the last sig fig
remains the same.
 34, 231 rounded to 3 sig figs 
34,200
 If it is 5 or greater, round up.
 Ex: 0.09246 rounded to 3 sig figs 
0.0925
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Practice Rounding (p 69)
 Round off each measurement to the number




of sig figs shown in parentheses.
= 314.7 meters
314.721 meters (four)
=0.0018 meter
0.001775 meter (two)
NOTE: The zeros are
8792 meters (two)
= 8800 meters IMPORTANT place
holders, but are not
SIGNIFICANT b/c
25,599 (four)
= 2.560 x 10
4
NOTE: Sometimes the only way to
show sig figs properly is to use
scientific notation!
they don’t contribute
to the precision of the
answer.
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Significant Numbers in Calculations
 A calculated answer cannot be more precise than the
measuring tool.
 A calculated answer must match the least precise
measurement.
 Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing
 If you must round to obtain the right # of sig figs, do
so after all calcs are complete
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Adding and Subtracting
The answer is rounded to the same PLACE as the
LEAST PRECISE measurement .
25.2 one decimal place
+ 1.34 two decimal places
26.54
answer 26.5 one decimal place
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Learning Check
In each calculation, round the answer to the correct
number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
2) 256.8
3) 257
B. 58.925 - 18.2
=
1) 40.725
2) 40.73
3) 40.7
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Multiplying and Dividing
Round (or add zeros) to the calculated
answer until you have the same number of
significant figures as the measurement with
the fewest significant figures.
Ex: 4.31 cm x 7.22 cm x 9 cm = 280.0638 cm3
= 300 cm3
3 SF
3 SF
1 SF
1 SF
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Learning Check
A. 2.19 X 4.2 =
1) 9
2) 9.2
B. 4.311 ÷ 0.07 =
1) 61.58
2) 62
C.
3) 9.198
3) 60
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11 3) 0.041
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Practice in Teams
Q#1:
8.3lb ÷ 9.102 in2 = 0.911887497
= 0.91 lb/in2
2 SF
4 SF
ANSWER: 2 SF
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Practice in Teams
3 SF
Q#2:
3 SF
63.2 m2 - 2.38 m2 = 11.05617161 m
5.501 m
4 SF
= 11.1 m
Answer: 3 SF
NOTE: When you have a mixture of +/- &
x/÷, the rule for x/÷ is used. This rule
says, “round to the same # of SF as the
measurement with the least # of SF.”
You only round
once! (YORO).
DON’T round
after you
subtract, then
AGAIN after
you divide.
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You Practice: SF Review WS
(Don’t Copy)
 #21, 22, 25,27,30,31,32,35,36,37,38,39 (12
problems)
34
Cover the variable
you are solving for
and perform the
operation with the
given amounts
Density = __Mass__
Volume
M
(Mass)
D = _M_
V
÷
NOTE: Put this
on your P. Table
D
(Density)
X
V
(Volume)
35
Common Units for Density
Probs (Copy onto P. Table)
 Volume = L (mL), cm3
 NOTE: 1 mL = 1 cm3
 Mass = g (kg, mg, etc.), lbs
36
Density Practice Problem #1
(p 91)
QUESTION: A copper penny has a mass of 3.1 g
and a volume of 0.35 cm3. What is the density
of copper?
SOLUTION:
Givens:
Unknown:
 mass = 3.1 g
density = ?
 Volume = 0.35 cm3
 Find equation and solve D = m/v
 D = 3.1 g /0.35 cm3
 D = 8.8571 g/cm3
37
Density Practice Problem #2
(p 92)
What is the volume of a pure silver coin that has
a mass of 14 g? The density of silver (Ag) is
10.5 g/cm3.
 Givens:
Unknown:
 Mass = 14 g
volume = ?
 Density = 10.5 g/cm3
 Find formula & derive it: D = M/V V = M/D
 Substitute values & solve V = 14 g
10.5 g/cm3
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UNITS OF MEASUREMENT
We use SI units — based on the metric
system (SI means Systeme Internationale)
Length
Meter, m
Mass
Kilogram, kg
Volume
Liter, L
Time
Seconds, s
Temperature
Celsius degrees, ˚C
kelvins, K
39
Metric Prefixes
Base unit
(100) goes
here
(g, m, L)
40
How to set up conversion
factors in the metric system
 If you always select the larger of the 2 units as
your “1” unit,
 Then the multiplier (on prefixes table) will
have a positive exponent.
Ex 1:
Compare Megagrams & grams. Which is larger?
Megagrams
1 Mg = 106 grams
This is our “1” unit
This is the multiplier
from our table
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Ex: Compare meters & millimeters
 Which is the larger of the 2 units?
meters
1 meter = 103 mm
This is your “1” unit
NOTE: when you look on your
prefixes chart, the “milli-”
multiplier is 10-3. When we use
the method of making the larger
unit the “1” unit, we always have
a positive exponent for our
multiplier.
42
Conversion Factors
Fractions in which the numerator and denominator are
EQUAL quantities expressed in different units
Example:
1 km = 103 m
Factors: 1 km
103 m
and 103 m
1 km
They don’t change the value of the measurement, just the units in which
it is expressed.
43
Conversion Factors
Fractions in which the numerator and denominator are
EQUAL quantities expressed in different units
Example:
1 hr. = 60 min
Factors: 1 hr.
and
60 min
60 min
1 hr.
They don’t change the value of the measurement, just the units in which
it is expressed.
44
Ex 1: How many millimeters
in 1205 meters?
4. Place units of the
unknown in the numerator
of the conversion factor. (if
1. Identify your given. Place it far left.
3
1205 m 10 mm
6
x10
= 1.205
_____mm
1m
(The given units are in the
NUMERATOR. Your goal is
to get rid of the units of your
given. How?)
you can find a relationship between
the 2 units. We can! 1m = 103 mm)
2. Identify your unknown. Place it far right.
3. Place the units of
the given in the
denominator of the
conversion factor!
5. Cancel
units & do the
math! (Sig
figs!)
45
Ex: Convert your weight from
pounds (lbs) to kg.
1. Identify your given. Place it far left.
150 lbs
1kg
= _____kg
68
2.2 lbs
The given units are in the
NUMERATOR. Your goal is
to get rid of the units of your
given. How?
4. Place units of the
unknown in the numerator
of the conversion factor. (if
you can find a relationship between
the 2 units. We can! 1kg = 2.2lb)
2. Identify your unknown. Place it far right.
3. Place the units of
the given in the
denominator of the
conversion factor!
5. Cancel
units & do the
math! (Sig
figs!)
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Ex 3: How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min
cancel
By using dimensional analysis, the UNITS ensure that you
have the conversion right side up, and the UNITS are
calculated as well as the numbers!
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Example #4: PLEASE COPY
How many seconds are in 1.4 days?
Unit plan: days
hr
min
seconds
1.4 days x 24 hr x _60min x 60 s =___s
1 day
1 hr
1 min
ANSWER: 120,960 s.
FINAL ANSWER (in sig figs) = 120,000 s
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