1. Scientific Notation

2. Two Parts of a Number Written in Scientific Notation
A single non zero digit followed by a decimal and all other significant digits.
9.98
Part 2
Times a multiple of 10
X 10n
n= the number of places the decimal must be moved.

3. Example
To write 530 miles in scientific notation, we move the decimal so that it follows the first non zero digit (5.30).
We moved the decimal 2 places to the left. Therefore, n=2.
n is positive because the number in regular notation is greater than 1.
5.30 x 102 miles
=5.30 x 10 x 10
= 5.30 x 100 = 530

4. Example
To write kg in scientific notation, we move the decimal so that it follows the first non zero digit (5.75).
We moved the decimal 1 place to the right. Therefore, n=1.
n is negative because the number in regular notation is less than 1.
5.75 x 10-1 kg
= 5.75 x kg
= kg

5. Multiplication
To multiply numbers in scientific notation, we multiply the first parts and add the powers of ten.
Calculate the net force acting on an automobile with a mass of 2.5 x 102 kg that is accelerating at a rate of 2.0 x 101 m/s2.
Force=mass x acceleration
F= (2.5 x 102 kg) x (2.0 x 101 m/s2)
F= (2.5 x 2.0) x 10(2+1) kgm/s2
F=5.0 x 103 kgm/s2

6. Division
To divide numbers in scientific notation, we divide the first parts and subtract the powers of ten.
Calculate the density of an object with a mass of 7.5 x 102 g that has a volume of 1.0 x 103 mL.
Density=mass / volume
D= (7.5 x 102 g) / (1.0 x 103ml)
F= (7.5/1.0) x 10(2-3) g/ml
F=7.5 x 10-1 g/ml