In all programs, the basic units are Force (Lb, kip, N, kN, etc.), Length (ft, in, m, mm, etc.), Time (second), and Temperature (F, C). Mass is a derived unit. CSI programs do not use Lb or kip for mass units, they are only used for force units.
Weight has units of [F], where F is force. CONSISTENT mass units are given by [F/(L/T^2)], where L is length, T is time, and the mass units are simply force divided by UNIT acceleration.
When F = N, the consistent mass unit is N*s^2/m = kg.
When F = Lb(force), the consistent mass unit is Lb(force)*s^2/ft = slug.
This is the mass that gives a force of 1 Lb(force) under a unit acceleration.
This same mass, when accelerated by gravity g, gives a force (its weight) of 32.2 Lb(force).
The mass called Lb(mass) is not a consistent unit. 1 slug = 32.2 Lb(mass)
See http://en.wikipedia.org/wiki/Pound, subtopic _Force, weight, and mass _for more information.
Weight density has units of [F/L^3], and consistent mass density has units of [(F/(L/T^2))/L^3] = [FT^2/L^4]
The relationship between weight and mass is W = M * g, all in consistent units.
Likewise, the relationship between weight density and mass density is w = m * g.
Now, let's start with weight density w = 150 Lb/ft^3. Here "Lb" is a force, Lb(force), and convert it to mass density in kip-in units. Note that "kip" is also a force. Proceeding:
m = w / g = 150 Lb/ft^3 / (32.2 ft/s^2) = 4.658 Lb*s^2/ft^4 * (kip / 1000 Lb) * (ft / 12 in)^4 = 2.246E-7 kip*s^2/in^4
The important key here is that Lb and kip are force units, not mass units.