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Warm Up • Simplify. 9 4 10 10 3 7 2 8 2 xz x yz 3 5 4 2 ( ) cp cp

8 5 Scientific Notation

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Page 1: 8 5 Scientific Notation

Warm Up

• Simplify.9

4

10

10

3 7

2

8

2

x z

x yz

35 4

2( )

c p

cp

Page 2: 8 5 Scientific Notation

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

Page 3: 8 5 Scientific Notation

Scientific Notation

Making the writing of

REALLY BIG NUMBERS

easier

And really small ones, too.

Page 4: 8 5 Scientific Notation

Approximate Distance to Betelgeuse

6,000,000,000,000,000

miles away

Page 5: 8 5 Scientific Notation

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

Page 6: 8 5 Scientific Notation

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

Page 7: 8 5 Scientific Notation

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?

Page 8: 8 5 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.

Page 9: 8 5 Scientific Notation

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

Page 10: 8 5 Scientific Notation

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.

Page 11: 8 5 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

Page 12: 8 5 Scientific Notation

Change us!

135,604,800,000

39,900,000,000,000

271,209,600

Click for the next slide’s answers

Page 13: 8 5 Scientific Notation

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

Page 14: 8 5 Scientific Notation

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

Page 15: 8 5 Scientific Notation

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

Page 16: 8 5 Scientific Notation

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

Page 17: 8 5 Scientific Notation

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

Page 18: 8 5 Scientific Notation

Try Some

• 0.00004588

• 0.000307

• 0.0027

• Convert to scientific notation.

Page 19: 8 5 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

Page 20: 8 5 Scientific Notation

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

Page 21: 8 5 Scientific Notation

Try One.

• (1.9 x 108)(2 x 1010)

• 1.9 x 2 = 3.8

Page 22: 8 5 Scientific Notation

Try One Answer

• (1.9 x 108)(2 x 1010)

• 1.9 x 2 = 3.8

Answer 3.8 x 10 18

Page 23: 8 5 Scientific Notation

Try a Division Statement

5

12

(16 x 10 )

(2 x 10 )

Page 24: 8 5 Scientific Notation

Division Statement Answer

57

12

(16 x 10 )8 10

(2 x 10 )x

Page 25: 8 5 Scientific Notation

Assignment

• Page 403: 15 – 55 odds

Page 26: 8 5 Scientific Notation