Scientific Notation

How far away is the nearest Star besides our Sun (Proxima Centauri)?

40 000 000 000 000 km(13 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 forma x 10n

where a is between 1 and 10and n is an integer (neg. and

pos. whole number)

Write the distance to Proxima Centauri in scientific notation.

40 000 000 000 000 kmWhere 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 4 and the 0

4.0,000,000,000,000.How many decimal places did you

move the decimal?13

When the original number is more than 1, the exponent is positive.

The answer in scientific notation is

4.0 X 1013

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02 x 10-8

The decimal was moved how many places?

8When the original number is less than 1, the exponent is negative.

10-8

Write 28750.9 in scientific notation.1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

Example 1Given: 289,800,000Use: 2.898Answer: 2.989 x 108

Example 2Given: 0.000567Use: 5.67Answer: 5.67 x 10-4

2) Express 1.8 x 10-4 in decimal notation.

0.000183) Express 4.58 x 106 in decimal

notation.4580000.

Write in PROPER scientific notation.(Notice the number is not between 1 and 10)

8) 234.6 x 109

2.345 x 1011

9) 0.0642 x 104

6.42 x 102

Write 531.42 x 105 in scientific notation.1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108

Example 3Given: 5.093 x 106

Answer: 5,093,000

Example 4Given: 1.976 x 10-4

Answer: 0.0001976

Significant Digits and Scientific NotationWhen trying to determine the number of

significant digits within scientific notation we leave it the way it is and follow the same rules and pretend the x 10n is not there.

E.g. 0.01130x10-4 has ___ significant digits5.3x1015 has ___ significant digits