Objective The student will be able to: express numbers in scientific and decimal notation. Mrs. M. Williams -8 th Mathematics

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is a number from 1 to 9 and n is an integer

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 10 23

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x 10 -8

Write in scientific notation x x x x 10 5

Now let’s go the other way…. We will go from Scientific Notation to Standard Notation (also called Decimal Notation)

2) Express 1.8 x in Standard notation ) Express 4.58 x 10 6 in Standard notation. 4,580,000

The number in scientific notation is 6 x The answer in standard notation is You try… Go from Scientific Notation to Standard Notation.

You try… Go from Standard Notation to Scientific Notation. The answer in standard notation is 1386 The answer in scientific notation is x 10 3

You try… Go from Scientific Notation to Decimal Notation. The answer in scientific notation is 8.28 x The answer in decimal notation is 82,800,000,000

Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x x ) x 10 4 on calculator: x 10 2

Write x 10 5 in scientific notation Correctly x x x x x x x 10 8

Write (2.8 x 10 3 )(5.1 x ) in scientific notation x x x x 10 11