Scientific Notation Created by A.Oman Ellerbruch.nmu.edu

Learning Target: I can write numbers in standard notation into scientific notation. I can write numbers in scientific notation into standard notation. I can multiply and divide numbers in scientific notation.

What is it used for? Scientific notation is a way that scientists and mathematicians use to deal with really, really small or really, really large numbers.

General Formula for Scientific Notation N X 10 x N is any number between 1 and 10, but not 10. X can be a positive (+) number or a negative (-) number

How do you know if the exponent is (+) or (-)? Is the number bigger than 1? If it is bigger than 1 (1500 or 250,000) = X is positive (+) If it is smaller than 1 (.00567 or .0028) = X is negative (-)

If you do not see a decimal, it is at the end. Example: Given: 246,000 Is the number bigger than 1?: Yes (+), exponent is positive Move: 2.46 How many places did you move the decimal place: 5 Answer: 2.46 X 10 5 If you do not see a decimal, it is at the end.

Another Example: Given: 0.000246 Is the number bigger than 1?: NO (-), exponent is negative Move: 2.46 How many places did it move?: 4 Answer: 2.46 X 10 -4

Your turn to try…don’t forget the following steps! Is the number bigger than 1? Yes = No = Shift the decimal point over until the number is between 1 and 10, but not 10. Count how many times you have to move the decimal. Write number in proper format: N x 10x

Converting from Scientific Notation to Real Number Look at the exponent (or X) on the 10. POSITIVE EXPONENT = move the decimal that many places to the right. NEGATIVE EXPONENT = move the decimal that many places to the left.

Example Given:5.079 X 106 Move: Right 6 places Answer: 5,079,000

Given: 4.8971 X 10-7 Move: Left 7 places Answer: .00000048971 Another Example Given: 4.8971 X 10-7 Move: Left 7 places Answer: .00000048971

Now your turn, ask your classmate if you need help! Practice Now your turn, ask your classmate if you need help! If you are still having problems, then ask us! Converting PDF

Correcting Improper Scientific Notation Given:5079 X 106 Move: 5.079 X 103 X 106 Answer: 5.079 X 109

Correcting Improper Scientific Notation Given:0.00235 X 106 Move: 2.35 X 10-3 X 106 Answer: 2.35 X 103

Now your turn, ask your classmate if you need help! Practice Now your turn, ask your classmate if you need help! If you are still having problems, then ask us! Converting PDF

Write 10 numbers that are really big or really small. HW Write 10 numbers that are really big or really small. It has to be about something in the real world. The national debt is $13,000,000.000.