Objectives: (1) To write a number in scientific notation. (2) To perform calculations with numbers written in scientific notation.

Scientific Notation A less confusing way of expressing very large or small numbers Example: 325,000,000,000,000 = 3.25 x = 8.6 x

How to convert to scientific notation 1.Convert to a number between 1 and 10 by moving the decimal point left or right. Examples: 45,000 = = 4.5

2. Write the number from step 1 followed by “x 10.” Examples: 45,000 = 4.5 x = 4.5 x 10

Number greater than one = positive exponent Number less than one = negative exponent 3. Write the number of spaces you moved the decimal point as an exponent. Examples: 45,000 = 4.5 x = 4.5 x Greater than 1 Less than 1

Practice 1.) 3,000 5.) ) ) 1,000 3.) ) ) 5,800,000 8.) 183,900,000,000

Answers 1.) 3 x ) 4.56 x ) x ) 5.8 x ) x ) 1.0 x ) 9.32 x ) x 10 11

Going Backwards… Positive Exponent = move the decimal right Negative Exponent = move the decimal left

Practice 1.) x ) 9.9 x ) 2.1 x ) 5 x ) x ) 9.44 x ) x ) 3.01 x 10 3

Answers 1.) x 10 5 = 602,300 2.) 9.9 x = ) 2.1 x 10 7 = 21,000,000 4.) 5 x 10 8 = 500,000,000 5.) x = ) 9.44 x 10 9 = 9,440,000,000 7.) x = ) 3.01 x 10 3 = 3,010

2.5 x 5.0 = = 31 Answer = 12.5 x  1.25 x 10 32

Practice

2.5 / 5.0 = – 14 = 3 Answer: 0.5 x 10 3  5.0 x 10 2

Practice