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 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?

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.

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

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

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

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? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

Soooo 137,000,000 can be rewritten as 1.37 X 108

Using scientific notation, rewrite the following numbers. 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

Convert these: 1.23 X 105 123,000 6.806 X 106 6,806,000

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

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

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

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?

Using Scientific Notation, rewrite the following numbers. 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

More Examples 4 X 10-4 2) 1.248 X 10-6 .000001248 3) 6.123 X 10-5 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

.000007 The nucleus of a human cell is about 7 X 10-6 meters in diameter. What is the length in standard notation? .000007

A ribosome, another part of a cell, is about 0 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

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