Scientific Notation express numbers in scientific and decimal

Scientific Notation -express numbers in scientific and decimal notation.

Part 1. 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 exponent

How wide is our universe? 210, 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 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. How many decimal places did you move the decimal? 23 The answer in scientific notation is 2. 1 x 1023

1) Express 0. 0000000902 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 9. 02 x 10 -8

NOTE: • If you are Beyonce, and moving the decimal point to the LEFT, the exponent will be POSITIVE! • If you are anti-Bey and moving the decimal point to the RIGHT, the exponent will be NEGATIVE!

EXAMPLES… write in scientific notation • • 1. 2. 3. 4. 3, 725, 000 0. 000316 14, 140, 000 0. 114

Part 2. Writing in Standard Form -if the problem is already written in scientific notation, you will have to write it in standard form

To write in standard form: • Take the decimal point and move it the number of spaces indicated by the exponent Ex. 2. 36 x 105…you will move the decimal point 5 places STANDARD = # LINE Negative Exponent move to the left Positive Exponent move to the right

Write 3. 27 x 10 -3 in standard notation. 1. 2. 3. 4. 327, 000 3, 270 0. 0327 0. 00327

2) Express 1. 8 x 10 -4 in decimal notation. 0. 00018 3) Express 4. 58 x 106 in decimal notation. 4, 580, 000

Part 3: Rewriting problems into proper scientific notation • Sometimes, problems will be written in improper scientific notation. • In order to fix it, you have to move the decimal into its proper location • When that happens, you will have to add onto the original exponent

Write 531. 42 x 105 in scientific notation. 531. 42 x 105 Since you moved the decimal point 2 places to the left, you add on 2 digits to the exponent 5. 3142 x 107

Write 0. 00042 x 108 in scientific notation. Since you moved the decimal point 4 places to the right, you subtract 4 digits to the exponent 4. 2 x 104