1. Scientific Notation Algebra Seminar

2. Objectives ► Write numbers in standard and scientific notation. ► Perform calculations with numbers in scientific notation.

3. What is Scientific Notation? ► A number expressed in the form: where Example: Neptune is 2,800,000,000 miles from the sun.

4. How do you write a number in scientific notation? Ex: 3,000,000,000,000 Where is the decimal point?. You move the decimal point to the left until the number in front of it is between 1 and 9. 3,000,000,000,000..

5. How do you write a number in scientific notation? Ex: 0.000063 You move the decimal point to the right until the number to the left of it is between 1 and 9. 0.000063 Notice that the exponent is negative!

6. Write in Scientific Notation 234,000,000 1. 23.4 x 10 7 23.4 x 10 723.4 x 10 7 2. 2.34 x 10 8 2.34 x 10 82.34 x 10 8 3. 234 x 10 6 234 x 10 6234 x 10 6 4. 2.34 x 10 -8 2.34 x 10 -82.34 x 10 -8

7. How to change numbers in scientific notation to standard notation. ► First, decide which way you are going to be moving your decimal point. Negative Exponent – move to the left Positive Exponent – move to the right Move the decimal point the number of the exponent. Ex: 6.35 x 10 4 = 1.82 x 10 -5 = 63,500 0.0000182

8. Write in standard notation ► 9.608 x 10 9 ► 3.5 x 10 -4 ► 8.3 x 10 -2 ► 5.07 x 10 6 9,608,000,000 0.00035 0.083 5,070,000

9. Operations with scientific notation. Adding: You just add the first numbers (4 x 10 4 ) + (9 x 10 4 ) = (4 + 9) x 10 4 = 13 x 10 4Subtracting: You just subtract the first numbers (8 x 10 4 ) - (2 x 10 4 ) = (8 - 2) x 10 4 = 6 x 10 4

10. Operations with scientific notation. Multiplying: Multiply the first numbers and then the second numbers. (7 x 10 2 )(4 x 10 5 ) = (7  4)(10 2  10 5 ) = 28 x 10 7 Write 28 in scientific notation. (2.8 x 10 1 ) x 10 7 Simplify. 2.8 x 10 8

11. Operations with scientific notation. Dividing: Divide the first numbers and then the second numbers. Simplify the exponents.