????????? x x x x x What do the numbers to the left have in common? They all start with a number between 1 and 10 They are all multiplied by the base power of 10 They all have exponent They describe numbers that are generally very large or very small They are written in scientific notationThey are written in scientific notation

Common Core Numbers 5 & 6 Express large and small numbers in scientific notation including use in real-world problems

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

One way people use scientific notation! 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.

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

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

Express in scientific notation. 1.8 x Express 4,580,000 in scientific notation x 10 6 NOTEBOOK EXAMPLES

Changing Numbers from Scientific Notation to Standard Notation Lets take 5.67 x 10 8 which is written in scientific notation. You want to know the actual number. So lets change it into standard form. You move your decimal 8 places to the right filling in zeros where you have no numbers. (See board for example) The final answer would be 567,000,000

Changing Numbers from Scientific Notation to Standard Notation Lets take x which is written in scientific notation. You want to know the actual number. So lets change it into standard form. You move your decimal 4 places to the left filling in zeros where you have no numbers. (See board for example) The final answer would be

You try a few! Write the numbers in standard form. (1) x 10 6 (2) x (3) 9.0 x ANSWERS (1) 2,093,000 (2) (3)

Comparing Numbers Which is larger? (A) 4.67 x (B) (C) 4/10,000 (D) 4.7 x The answer is (A) 4.67 x How did you figure it out? You could have written your answers in standard notation or just know -4 is bigger than -5 on the number line

PRACTICE PROBLEMS Pages You will have to apply your knowledge on #9