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Scientific Notation
Scientist use special notation to express very large or very small numbers.
Example I: 300,000,000 g can be written as…3 x 108 g
Ex II: 1,007,000,000 sec can be written as… 1.007 x 109 sec
Ex III: 0.000 000 000 004 76 mL can be written as… 4.76 x 10-12 mL
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.
Before we take this trip, let’s review significant figures…
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
5
53
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.
Before we take this trip, let’s review significant figures…
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.
Let’s say you want to travel from Oracle Jct to Casa Grande...
You must travel through Tucson… a two part trip.
Now back to our road trip…
OK…Lets talk about making maps and solving
conversion problems. The method we use is called the
“Factor-Label” method, a.k.a. dimensional analysis.
gallons kildurkins
For Example: Given 1 kildurkin = 18 gallons
How many kildurkins is 14 gallons?
1 kildurkins
18 gallons
14 gallons =0.78
kildurkins
gallons kildurkins
Also given: 1 hogshead = 63 gallons
farkins
hogshead
1 barrel = 3.3 bushels
bushel barrel
1 bushel = 8 gallons
gallons kildurkins farkins
hogshead
bushel barrel
Now, Lets solve a problem.
How many hogsheads are 14 barrels?
Given: Start Here
Finish HereThe trip will require 3 transitions
1
2
3
gallons
hogshead
bushel barrel
How many hogsheads are 14 barrels?
1
2
3
Given fromcoming
togoing
fromcoming
togoing
fromcoming
togoing
14 barrels 3.3 bushels1
barrel
8 gallons1 bushel
1 hogshead63 gallons
= 5.9 hogsheads
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 bushels8 gallons
1 bushel
1 kildurkin18 gallons
2 farkins
1 kildurkin
= 2.67 farkins