1. E XPONENTS AND S CIENTIFIC N OTATION Method of writing very large or very small numbers to make mathematical manipulations easier Numbers are expressed as some quantity between 1 & 10 multiplied by 10 raised to some exponent N = A x 10 n

2. Every non-zero number can be written in scientific notation. For example

3. M ORE EXAMPLES The speed of light it approx. 30,000,000,000 cm/s in scientific notation we would move the decimal 10 places to the left and would express the number as 3 x 10 10 cm/s (only sig figs are expressed)

4. The diameter of an atom = 0.0000000001m In scientific notation we would move the decimal place 10 places to the right and the measurement would be expressed as 1 x 10 -10 m

5. P ARTS OF A NUMBER IN SCIENTIFIC NOTATION A x 10 n A = coefficient between 1 & 9, can be positive or negative (must be ≥ 1 and < 10) 10 = called the base n = integer, positive, negative or zero

6. C ONVERTING TO S CIENTIFIC N OTATION To find “A” - move decimal point to the left until one digit remains to the left of the decimal point To find “n” count how many places you moved the decimal “n” is positive if – you moved the decimal to the left if the number in decimal form was greater than 10 “n” is negative if – you moved the decimal to the right if the number in decimal form was less than 1 A x 10 n

7. C ONVERTING TO S CIENTIFIC N OTATION For numbers less than 1 1. 1. To find “A” - move decimal point to the right until one digit remains to the right of the decimal point 2. To find “n” count how many places you moved the decimal 3. “n” is negative if – you moved the decimal to the right if the number in decimal form was less than 1

8. F OR E XAMPLE : 456,000 = 4.56 x 10 5 0.0000456 = 4.56 x 10 -5 Only sig figs are included !!

9. Numbers 1 – 9.999999 No conversion is necessary Written as A x 10 0 (10 0 = 1) 3.45 to scientific notation 3.45 = 3.45 x 10 0

10. C ONVERT FROM D ECIMAL FORM TO S CIENTIFIC N OTATION (a) 93,000,000 (b).00005144 (c) -33,452.8

11. C ONVERT FROM S CIENTIFIC N OTATION TO D ECIMAL F ORM

12. W ATCH THE ZEROS ! 0.000068120 m (5 sig figs) = 6.8120 x 10 -5 0.006060 g (4 sig figs) = 6.060 x 10 -3 52.0030 L (6 sig figs) = 5.20030 x 10 1 676.0 cm (4 sig figs) = 6.760 x 10 2

13. D OUBLE CHECK !! Correct way to write: 5.533 x 10 5 Incorrect way to write: 55.33 x 10 5 Do in class exercises