Warm Up

• Simplify.9

4

10

10

3 7

2

8

2

x z

x yz

35 4

2( )

c p

cp

Warm Up

• Simplify.9

54

1010 100,000

10

3 7 6

2

8 4

2

x z xz

x yz y

35 4 15 129 6

2 6 6( )

c p c pc p

cp c p

Scientific Notation

Making the writing of

REALLY BIG NUMBERS

easier

And really small ones, too.

Approximate Distance to Betelgeuse

6,000,000,000,000,000

miles away

Approximate Distance to Proxima Centauri

• 4.3 light years

• 4.3 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately

• 135,604,800,000 miles

Or

• 39,900,000,000,000 kmGraphic from http://heasarc.gsfc.nasa.gov/docs/cosmic/nearest_star_info.html

Approximate Distance to Sirius A

• 4.3 light years

• 8.6 x 186, 000 m/s x 60s x 60 m x 24 hr x 365 days is approximately…

• 271,209,600,000 miles

Image from space.com

Sirius iscalled the Dog Star

Big Numbers to write with less zeros

• 271,209,600,000

• 135,604,800,000

• 39,900,000,000,000

• What should we use?

• How about Scientific Notation?

271,209,600,000

• Step one:

• How many places can we move the decimal to just inside the left most digit?

• 271,209,600,000

• Looks like eleven places.

Now insert the new decimal place and eliminate the end zeros.

• 2.71209600000

and eliminate the end zeros.• 2.712096

• To make 2.712096 equal to 271,209,600,000 we use a power of 10.

• In this case, 1011

2.712096 x 10 ?

• We can multiply 2.712096 x 100,000,000,000 to get back to our original number.

• 100,000,000,000 is 1011

• 2.712096x1011 is written in scientific notation.

Rules for Scientific Notation

• The first number MUST be between 1 and 10

• The operation is multiplication• The second number is a power of 10.

• Check this with the above rules:• .9808 x 105

• Better: 9.808 x 104

Change us!

135,604,800,000

39,900,000,000,000

271,209,600

Click for the next slide’s answers

Change us to these answers.

135,604,800,000 =

1.356048 x 1011

39,900,000,000,000 =

3.99 x 1013

271,209,600 =

2.712096 x 108

Let’s review

To change 34,000,000,000,000,000 to scientific notation.

Count the places from the far right to the place just to the right of the left-most digit (3). That’s 16 places.

That’s the power of ten. In this case, 1016

Get rid of the extra unneeded zeros and multiply by the chosen power of ten.

3.4 x 1016

Very Small Numbers

• Let’s try 0.000079 as a number in scientific notation.

• Recall that negative exponents show fractions.

• The above number as a fraction would be seventy-nine millionths.

79

1,000,000

How many places do we need to move the decimal. 0.000079

• We’ll end up with 7.9

(between 1 and 10).

• 7.9 x 10 -?

• 7.9 x 10 -5

Write in scientific notation: 0.003011

• How far to move the decimal?

• What number will be between 1 and 10?

• Since the number is less than one, we’ll have a negative decimal.

• 3.011 x 10 -3

Try Some

• 0.00004588

• 0.000307

• 0.0027

• Convert to scientific notation.

Try Some Answers

• 0.00004588 = 4.588 x 10-5

• 0.000307 = 3.07 x 10 -4

• 0.0027 = 2.7 x 10 -3

How do I combine numbers in scientific notation?

• (8.2 x 106)(3.1 x 106)

• 8.2 x 3.1 = 25.42

• 106 x 106 = 10 12

• 25.42 x 10 12 needs adjustment.(The 25.42 is NOT between 1 and 10)

• 2.542 x 10 13

Try One.

• (1.9 x 108)(2 x 1010)

• 1.9 x 2 = 3.8

Try One Answer

• (1.9 x 108)(2 x 1010)

• 1.9 x 2 = 3.8

Answer 3.8 x 10 18

Try a Division Statement

5

12

(16 x 10 )

(2 x 10 )

Division Statement Answer

57

12

(16 x 10 )8 10

(2 x 10 )x

Assignment

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