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Performing these conversions is a lot like going on a road trip.

Performing these conversions is a lot like going on a road trip

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Performing these conversions is a lot like going on a road

trip.

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…

Rule: You must stay on the roads

X

Rule: You need a map. Sometimes the map can be in your head. But, not at first.

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

This is our map.

gallons kildurkins

For Example: Given 1 kildurkin = 18 gallons

How many kildurkins is 14 gallons?

1 kildurkins

18 gallons

14 gallons =0.78

kildurkins

General Format...

going to

coming from

given

gallons kildurkins

Also given: 2 farkins = 1 kildurkin

farkins

Let’s expand the map...

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

Wow! How Cool Is That!