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SCIENTIFIC NOTATION

A QUICK WAY TO WRITE

REALLY, REALLY BIG

OR

REALLY, REALLY SMALL NUMBERS.

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Scientists �are Lazy!!!

They decided that by using powers of 10, they can create short versions of long numbers.

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Rules for Scientific Notation

To be in proper scientific notation the number must be written with

* a number between 1 and 10

* and multiplied by a power of

ten

23 X 105 is not in proper scientific notation. Why?

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Soooo

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137,000,000 can be rewritten as

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1.37 X 108

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Now You Try

Using scientific notation, rewrite the following numbers.

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347,000

3.47 X 105

902,000,000

9.02 X 108

61,400

6.14 X 104

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Convert these:

1.23 X 10-5

.0000123

6.806 X 10-6

.000006806

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Try These

4,000

4 X 103

2.48 X 103

2,480

6.123 X 106

6,123,000

306,000,000

3.06 X 108

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In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation.

1.5 X 107

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  • The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form.

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12,916,000 acres

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Why does a negative exponent give us a small number?

10000 = 10 x 10 x 10 x 10 = 104

1000 = 10 x 10 x 10 = 103

100 = 10 x 10 = 102

10 = 101

1 = 100

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Do you see a pattern?

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Sooooo

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= 10-1

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= = 10-2

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= = 10-3

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= = 10-4

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Your Turn

Using Scientific Notation,

rewrite the following numbers.

0.000882

8.82 X 10-4

0.00000059

5.9 X 10-7

0.00004

4 X 10-5

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More Examples�

1) 0.0004

4 X 10-4

2) 1.248 X 10-6

.000001248

3) 6.123 X 10-5

.00006123

4) 0.00000306

3.06 X 10-6

5) 0.000892

8.92 X 10-4

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The nucleus of a human cell is about

7 X 10-6 meters in diameter. What is the length in standard notation?

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.000007�

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A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation.

3 X 10-9