Mechanics: Newton's 3 Laws of Motion and Measurements

 Law 1: A particle at rest remains that way if not subjected to an unbalanced force. 

Law 2: A particle acted upon an unbalanced force F experiences acceleration that has the same direction as the force and magnitude that is directly proportional to the force. That is, F = ma. 

Law 3: Mutual forces of action and reaction between particles are equal/opposite and colinear. 

Newton's Law of Gravitational Attraction:

The Gravitational attraction between 2 particles m1 and m2 is F = (G*m1*m2)/(r^2) where G is the constant of gravity, F is the force of gravity, m1 and m2 are the masses of the particles, and r is the distance between the particles. G is (66.73 * (10 ^ -12) m^3) / (kg * (s ^ 2)).

Now weight is the force between the earth and the particle where we assume m2 to be the mass of the earth and we assume gravity is 45 degrees on earth level as (G*m1*ME)/(r^2) where ME is the mass of the earth. Gravity is 9.81 m/(s^2) or 32 ft/(s^2) and 1 slug is 1g s^2/ft.

We represent everything is base 10. For example if we want to represent 23400 in 5 significant figures, we basically want to put 2.3400 * 10^4. 3 Significant digits are represented through 23.4 * (10^3). Zero's in front are not significant. Don't round a 5 if the number in front of the 5 is even, otherwise, you can round it up.