3. Why use scientific notation? We use very big numbers and very small numbers in chemistry. It’s hard to do computations with numbers that have lots of zeros in them. Hard to compare data meaningfully when you are grappling with lots of zeros.

4. Conventional Notation 0.000007890145000000000.000432044 0.000000063333990000000.000485945 0.000000054643890000000.000598458 0.000000027384800000000.000989593 0.000000333145430000000.000009032

5. Scientific Notation productThe number is written as the product of two other numbers: not –A number between 1 and 10 (not 10) and –A power of 10

6. The exponents greater positiveFor numbers greater than 1, the exponent will always be positive when you use scientific notation. between negativeFor numbers between 0 and 1, the exponent is negative! notA negative exponent does not make the number negative.

7. front The only way to make the number negative in scientific notation is to put a negative sign in front of the number!! -4.8 X 102 is a negative number. 5.3 X 10-1 is a positive number.

8. conventional to scientific notation Converting conventional to scientific notation  1exponent positive For numbers  1, the exponent will be positive. Count how many places the decimal is moved. 329  3.29 X 10 2

9. conventional to scientific notation Converting conventional to scientific notation between 0 and 1 exponentnegative For numbers between 0 and 1, the exponent will be negative. Count how many places the decimal is moved. 0.00045  4.5 X 10 -4

10. scientific to conventional Converting scientific to conventional notation If the exponent is positive, the number  1, so move the decimal point right. 3.784 X 10 5  378400

11. scientific to conventional Converting scientific to conventional notation If the exponent is negative, the number is between 0 and 1 so move the decimal point to the left. 2.75 X 10 -3  0.00275

12. Multiplication Multiply numbers Add exponents Convert to proper form if necessary –If you move the decimal left, add to the exponent. –If you move the decimal right, subtract from the exponent.

13. Practice! (2 X 10 3 )(4 X 10 2 ) = (4 X 10 2 )(6 X 10 4 ) = (3 X 10 4 )(5 X 10 -2 ) = 8 X 10 5 24 X 10 6 = 2.4 X 10 7 15 X 10 2 = 1.5 X 10 3

14. Division Divide numbers Subtract exponents Convert to proper form if necessary –If you move the decimal left, add to the exponent. –If you move the decimal right, subtract from the exponent.

15. 6 X 10 2  9 X 10 -3 =0.66  X 10 5 = 6.6 X 10 4 = 7 X 10 4

16. Addition and Subtraction Convert to common exponent if necessary –If you have to increase the exponent, move the decimal to the left. –If you have to decrease the exponent, move the decimal to the right. Add or subtract numbers Maintain exponent Convert to proper form if necessary

17. 2.6 X 10 -2 + 3.7 X 10 -2 ______________ 6.3 X 10 -2 5.5 X 10 -4 + 7.5 X 10 -5 ______________  5.5 X 10 -4 + X 10 -4.75 _____________ 6.25 X 10 -4