SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS. Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers. Rules for Scientific Notation
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SCIENTIFIC NOTATION A QUICK WAY TO WRITE
REALLY, REALLY BIG
OR REALLY, REALLY SMALL NUMBERS.<br>
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Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers.<br>
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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?<br>
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How wide is our universe? 210,000,000,000,000,000,000,000 miles
(22 zeros)
This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.<br>
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Scientific Notation A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer<br>
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Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1<br>
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2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal?
23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023<br>
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1) Express 0.0000000902 in scientific notation. Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places?
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When the original number is less than 1, the exponent is negative.
9.02 x 10-8<br>
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Soooo 137,000,000 can be rewritten as
1.37 X 108<br>
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Now You Try Using scientific notation, rewrite the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104<br>
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Convert these: 1.23 X 105
123,000
6.806 X 106
6,806,000<br>
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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<br>
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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<br>
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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.
12,916,000 acres<br>
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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
Do you see a pattern?<br>
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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<br>
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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<br>
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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?
.000007<br>
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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<br>
