unit 1 scientific notation/powers of 10 significant figures dimensional analysis (factor label...
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Unit 1
•Scientific Notation/Powers of 10•Significant Figures•Dimensional Analysis (Factor Label Method)
Scientific Notation
Scientist use special notation to express very large or very small numbers.
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)
basic unit
centi-
hecto-
deca-
kilo-
deci-
milli-
1
10-1
10-3
10-2
103
102
101
To convert, move the decimal place the number of stairs you step on in the direction you are traveling OR use dimensional analysis.
Example:
3.75 km = ? mm
? = 3,750,000 mm
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: 300,700Decimal Absent… Atlantic (right)… 4 sig. figs. (the last 2 zeros are PLACE HOLDERS)
REVIEW
1) 0.0034050 L ___________2) 33.600 m ___________3) 7500.0 g ___________4) 47,900 mm ___________5) 7,000,000,001 miles ___________6) 8.07 Hz ___________
Determine how many significant figures are in each of the following measurements.
5 (the first 3 zeros are PLACE
HOLDERS)
5
53 (the last 2 zeros are PLACE
HOLDERS)
10
3
More practice…
7) 366.2 L ___________8) 9,047,022 mg ___________
9) 12.76 g ___________10) 999.9 J ___________
Round the following measurements off so that they each contain 3 significant figures.
366 L9,050,000
mg12.8 g1.00 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
11)36.57 m / 3.21 s = ___________12)41.376g + 13.3g + 42.9g=___________
13)5.67 m x 13.44 m ___________14)(5.83 m/ 2.67 s) /2.1 s ___________15)9.374 V x 6 ___________
Perform the prescribed operations. Round your answers to the proper # of sig. figs.
11.4 m/s97.6 g
76.2 m2
1.0 m/s2
60 VFrom 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
DIMENSIONAL ANALYSISDIMENSIONAL ANALYSIS
How old are you in seconds?How old are you in seconds?
Go from number of years to number of Go from number of years to number of seconds.seconds.
EX: 15 years old EX: 15 years old _____ seconds old. _____ seconds old.
To do this, you need to use CONVERSION FACTORS To do this, you need to use CONVERSION FACTORS (a ratio of equivalent values used to express the (a ratio of equivalent values used to express the same quantity in same quantity in different unitsdifferent units))
GIVEN INFORMATIONGIVEN INFORMATION
1 kildurkin = 18 gallons1 kildurkin = 18 gallons
2 farkins = 1 kildurkin2 farkins = 1 kildurkin
1 hogshead = 63 gallons1 hogshead = 63 gallons
1 barrel = 3.3 bushels1 barrel = 3.3 bushels
1 bushel = 8 gallons1 bushel = 8 gallons
Make a UNIT CONVERSION Make a UNIT CONVERSION MAPMAP
Draw connections between the units in the Draw connections between the units in the conversion factors…conversion factors…
(as you draw connections, check that (as you draw connections, check that conversion factor off the list)conversion factor off the list)
It’s kind of like a road map…
Let’s say you want to travel from Oracle Jct to Casa Grande...
You must travel through Tucson… a two part trip.
ROAD TRIP!!!
gallons kildurkins farkins
hogshead
bushel barrel
Now you try one. How many farkins is 3.00 bushels?
Start Here
End Here
This will require 3 Conversions.
bushels gallons kildurkins farkins
3.00 bushels 8.0 gallons1.0 bushel
1.0 kildurkin18 gallons
2.0 farkins
1.0 kildurkin
= 2.67 farkins
X XX
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