Opener:  When you’re taking notes, if you have to write the same big word or words over and over again….do you write it out every time? How do you make it quicker?  If some random person looked at your notes would they be able to read them? Why or why not?

 Scientific Notation Shorthand method of writing very large and very small numbers based on powers of 10

 For example: = x = 1.34 x The decimal goes after the first whole number The superscript tells you how many decimal places to move, and in what direction.

7.3x10 4 = 7.3 x 10,000 = 73,000  (to write the number out longhand, the decimal point moved 4 places to the right)  9.4x10 -3 = 9.4 x =  ( to write the number out longhand, the decimal point moved 3 places to the left)

 Practice  Write the following numbers in scientific notation; 94,320,000, ,000,000,000,000,000, (9 zeros after the decimal)  Write the following numbers out the long way; 7.14 x x x x 10 -4

Math with exponents When adding and subtracting numbers with exponents, you must first convert all numbers to have the same exponent. 1) 2.81x x10 8 = 0.281x x10 8 = 4.601x10 8

2) 9.32x x10 20 =

2 ) 9.32x x10 20 = 9.32x x10 21 =

2 ) 9.32x x10 20 = 9.32x x10 21 = 9.166x10 21

When multiplying numbers with exponents, you simply multiply the coefficients and add the exponents. 3 ) (1.21x10 14 )(3.42x10 12 ) = (1.21 x 3.42) x10 (14+12) = 4.14x10 26

When dividing numbers with exponents, you divide the coefficients and subtract the exponents. 4) (4.19x10 7 ) / (2.16x10 3 ) = (4.19/2.16) x10 (7-3) = 1.94x10 4

Now you try a few… 8.46x x10 11 = 9.84x x10 15 = (2.91x10 6 )(4.33x10 4 ) = 7.94x10 10 ∕ 3.24x10 3 =

Closer:  List the steps involved in multiplying two numbers that have exponents.  How would those steps change if you were dividing the numbers instead?