Physics
Vandebilt Catholic High School
Walt Dupre

1. Scientific notation is a shorthand way of expressing numbers that replaces decimal places with powers of ten.

N X 10^e (Where "N" is the coefficient and "e" is the exponent.)

2. How to express numbers in scientific notation
    
1. Move the decimal until only one digit is to the left of the decimal.
2. Count the number of places the decimal was moved and use this number as your exponent.
3. The exponent is positive if the decimal was moved to the left.
4. The exponent is negative if the decimal was moved to the right.
5. Example: 345000 is expressed as 3.45 X 10⁵
3. How to expand numbers from scientific notation
1. Add decimal places, with zeroes as place holders, to equal the number in the exponent.
2. Move the decimal to the left if the exponent was negative.
3. Move the decimal to the right if the exponent was positive.
4. Example: 3.45 X 10^-5 is 0.0000345

4. Addition and subtraction in scientific notation
1. If the exponents are the same simply add/subtract the coefficients and keep the same exponent.
2. If the exponents are different make them the same by moving the decimal of the smaller number to the left until the exponents match and then perform the operation.
3. Remember that your final answer must have only one non-zero digit to the left of the decimal.
4. Example: 3.0 X 10³ + 4.0 X 10² = ?
   Before beginning the numbers should be adjusted as such:
   3.0 X 10³ + 0.40 X 10³ = 3.4 X 10³

5. Multiplication and division in scientific notation
1. To multiply – multiply the coefficients and add the exponents
2. To divide – divide the coefficients and subtract the exponents
3. Remember that your final answer must have only one non-zero digit to the left of the decimal.
4. Example: 6.0 X 10² / 2.0 X 10⁵ = ?
   Divide the coefficients: 6.0 / 2.0 = 3.0
   Subtract the exponents: 2 – 5 = -3
   Final Answer: 3.0 X 10^-3
Return to the Physics table of contents