Transcript Significant Figures

Unit 1
•Scientific Notation/Powers
of 10
•Significant Figures
•Dimensional Analysis
(Factor Label Method)
Scientific Notation
Scientist use special notation to express
large or very small numbers.
very
Example I: 300,000,000 m/sec can be written as…
3 x 108 m/sec
Ex II: 1,007,000,000 sec can be written as…
1.007 x 109 sec
Ex III: 0.000 000 000 004 76 m can be written as…
4.76 x 10-12 m
Converting Metric Measurements
(PART 4 of Things to Know and Love)
To convert, move the decimal
place the number of stairs you
step on in the direction you are
traveling OR use dimensional
analysis.
kilo-
103
hecto-
102
deca-
101
Example:
3.75 km = ? mm
? = 3,750,000 mm
basic
unit
1
deci-
10-1
centi-
10-2
milli-
10-3
Video
Powers of Ten
SIGNIFICANT FIGURES
Scientists indicate the precision of
measurements by the number of digits they
report = sig. figs.
A value of 3.52 g is more precise than a value of
3.5 g
All known digits plus one estimated digit
** the equipment used for a measurement will
determine the number of sig. figs.
Significant Figures
Atlantic - Pacific Rule:
Decimal Present: Count from the Pacific side
Decimal Absent: Count from the Atlantic side
Start counting at the first non-zero number and
count until you reach the end of the number
Ex. I: 3.00700
Decimal Present… Pacific (left)… 6 sig. figs.
Ex. II: 300,700
Decimal Absent… Atlantic (right)… 4 sig. figs.
(the last 2 zeros are PLACE HOLDERS)
REVIEW
Determine how many significant figures are in
each of the following measurements.
1)
2)
3)
4)
5)
6)
0.0034050 L
33.600 m
7500.0 g
47,900 mm
7,000,000,001 miles
8.07 Hz
5
___________
5
___________
___________
5
3
___________
10
___________
___________
3
(the first 3 zeros are PLACE
HOLDERS)
(the last 2 zeros are PLACE
HOLDERS)
More practice…
Round the following measurements off so that
they each contain 3 significant figures.
7) 366.2 L
8) 9,047,022 mg
9) 12.76 g
10) 999.9 J
___________
366 L
9,050,000
mg
___________
___________
12.8 g
1.00 x 103 J
___________
Notice this one must be in scientific
notation to have 3 sig. figs.
Significant Figures in Calculations
When multiplying and dividing, limit
and round to the least number of
significant figures in any of the
factors.
Example:
23.0 x 432 x 19 = 188,784 = 190,000
The answer is expressed as 190,000 or
1.9 x 105 since 19 has only two sig. figs.
Significant Figures in Calculations
When adding and subtracting, limit and
round your answer to the least number of
decimal places in any of the numbers
involved in the calculation.
Example:
123.25 + 46.0 +86.257 = 255.507 = 255.5
The answer is expressed as 255.5 since 46.0
has only one decimal place.
REVIEW
Perform the prescribed operations. Round your
answers to the proper # of sig. figs.
11.4 m/s
11)36.57 m / 3.21 s =
___________
97.6 g
12)41.376g + 13.3g + 42.9g=___________
76.2 m2
13)5.67 m x 13.44 m
___________
1.0 m/s2
14)(5.83 m/ 2.67 s) /2.1 s
___________
60 V
15)9.374 V x 6
___________
From now on, we will round all our answers
to the correct # of significant figures.
EXTRA REVIEW
Using a calculator for EXPONONETS
(EE, EXP or x10x button)
Example 1:
(5.02 x 10-3) x (6.3369 x 105)
= 3181.1238
*put in correct sig figs
= 3 sig figs
= 3180 or 3.18 x 103
Example 2 (use EE button!)
(2.99 x 106) x (2.334 x 10-3) =
= 6978.66
• 3 sig figs
• 6980
DIMENSIONAL ANALYSIS
 How

old are you in seconds?
Go from number of years to number of
seconds.
EX: 15 years old  _____ seconds old.
To do this, you need to use CONVERSION FACTORS
(a ratio of equivalent values used to express the
same quantity in different units)
Given Information: NOTETAKERS
General Format...
given
X
going to
coming from
=
GIVEN INFORMATION
1 kildurkin = 18 gallons
2 farkins = 1 kildurkin
1 hogshead = 63 gallons
1 barrel = 3.3 bushels
1 bushel = 8 gallons
Make a UNIT CONVERSION
MAP
Draw connections between the units in the
conversion factors…
(as you draw connections, check that
conversion factor off the list)
It’s kind of like a road map…
hogshead
gallons
bushel
barrel
kildurkins
farkins
Performing these
conversions is a lot like
going on a road trip.
ROAD TRIP!!!
Let’s say you want to travel from Oracle Jct to Casa Grande...
You must travel
through Tucson…
a two part trip.
Rule: You must stay on the roads &
REMEMBER SIG FIGS!!!
DO NOT GO OFF ROAD! 
Rule: You need a map. Sometimes the map can be in
your head. But, not at first. (show all work!!)
Let’s calculate
Convert 14 gallons to kildurkins
Convert 14 barrels to hogshead
Convert 3.00 bushels to farkins
Now you try one. How many farkins is
3.00 bushels?
End Here
hogshead
gallons
kildurkins
farkins
Start Here
bushel
barrel
This will require 3
Conversions.
bushels
3.00 bushels
gallons
kildurkins
farkins
8.0 gallons 1.0 kildurkin 2.0 farkins
X
X
X
1.0 bushel
18 gallons
1.0 kildurkin
= 2.67 farkins
Wow! How
Cool Is That!
Handout: Fun Factor Label
Handout
Piece of lined paper (landscape format)
Front is web for Distance and back is for Vol.
Conversion Factors: change 10-10 to
1 x 10-10
Let’s do league  km  m  cm to start
You finish web, then do #3,6,7,9
Then do vol. web
Then finish questions #4, 5, 8, 10
FINISH FOR HW