Unit 1 Scientific Notation/Powers of 10 Significant Figures Dimensional Analysis (Factor Label Method)

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

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: 300,700Decimal 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

Example 2 (use EE button!)

(2.99 x 106) x (2.334 x 10-3) =

= 6978.66

• 3 sig figs• 6980

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 Information: NOTETAKERS

General Format...

going to

coming from

givenX =

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…

gallons kildurkins farkins

hogshead

bushel barrel

Performing these conversions is a lot like going on a road

trip.

Let’s say you want to travel from Oracle Jct to Casa Grande...

You must travel through Tucson… a two part trip.

ROAD TRIP!!!

Rule: You must stay on the roads & REMEMBER SIG FIGS!!!

XDO 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

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

Wow! How Cool Is That!

Handout: Fun Factor Label

HandoutPiece 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 startYou finish web, then do #3,6,7,9Then do vol. webThen finish questions #4, 5, 8, 10FINISH FOR HW