scientific notation way to simplify big and small numbers

Scientific Notation

Way to simplify BIG and small numbers

Scientific Notation Coefficient x 10 exponent

602000000000000000000000 can be

6.02 x 1023

exponentcoefficient

Scientific Notation Coefficient x 10 exponent

Coefficient MUST be between 1 and 9

Exponent can be either positive or negative+ exponent large # (> 1)- exponent small # (< 1)

Scientific Notation

Convert the following into of scientific notation

35893 = ____________3.5893 x 104

Your turn!

0.00548 = ___________

10.25 = ___________

5.48 x 10-3

1.025 x 101

Scientific Notation

Convert the following out of scientific notation

2.579 x 104 = ________25790

8.647 x 10-5 = ________0.00008647

Put into Scientific Notation

Put INTO Sci. Not.

Convert out of Sci.Not.

Dimensional Analysis

Used to convert between unitsYou need to use a conversion factor

Conversion Factor

Ratio equal to “1” Contains the unit that you currently have (given in problem) and the unit that you want to convert to

Examples:

12 inches = 1 foot

60 seconds = 1 minute

12 inches1 foot 12 inches

1 footOR

60 seconds1 minute 60 seconds

1 minuteOR

Dimensional Analysis Conversion

Unit thatyou have

Unit thatyou have

Unit that you want

=Unit thatYou want

X

T-diagramConversionFactor

Single-step conversions

30 seconds = ? minutes

30 seconds

60 seconds

1 minute= 0.5 minute

Example

How many inches are in 3.7 feet? (12 inches = 1 ft)3.7 ft

1 ft

12 in = 44 in

Multi-Step ConversionThe conversion factor does NOT contain both the unit that you have and the unit that you want.

The unit conversion requires multiple (more than one) steps.

Example How many Liters are there in 8.2 quarts?

8.2 qt 32 oz

1 qt=

Conversion factors:1 qt = 32 oz1 qt = .94 Liters

32 oz

.94 L

= 7.71 Liters

You can do this!How many minutes are in 2 days?

(given) 2 days

You can do this!How many minutes are in 2 days?

(given) 2 days

(given) 1 day

24 hours

1 hour

60 minutes

= 2880 minutes

BUT… since there is only 1 digit in the given, there can only be 1 digit in the answer so…

= 3,000 minutes

Examples

Last one smarty pants!How many seconds are in 2 decades?

Last one smarty pants!How many seconds are in 2 decades?

2 decades

1 day1 year1 decade

24 hours365.25 days

10 years

1 minute1 hour

60 seconds

60 minutes

= 631,152,000 secondsBUT… since there is only 1 digit in the given, there

can only be 1 digit in the answer so…= 600,000,000

secondsNow in scientific notation… = 6 x 108 seconds

The Fundamental SI Units (le Système International, SI)

Physical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance

mole mol

Luminous Intensity candela cd

SI PrefixesCommon to Chemistry

Prefix Unit Abbr. Exponent

Kilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Nano n 10-9