What is the inverse of 466ft^2/gal?

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The discussion revolves around converting the coverage of house paint from 466 ft²/gal to square meters per liter and an SI unit. The correct conversion yields 11.44 m²/L and 11440 m⁻¹. The main confusion arises in determining the inverse of 466 ft²/gal, where the initial calculation of 0.002 gal/ft² is questioned for its accuracy. It is suggested that the issue may relate to significant figures, as 0.002 only has one significant digit compared to the original value's three. Clarification on the correct inverse unit, potentially in liters/m², is sought.
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The description for a certain brand of house paint claims a coverage of 466 ft2/gal. (a) Express this quantity in square meters per liter. (b) Express this quantity in an SI unit (see Appendices A and D). (c) What is the inverse of the original quantity?

I got answers for a) and b).

a) 466ft^2/gal x 1m^2/10.76ft^2 x 1 gal/231in^3 x 61.02in^3/1L = 11.44 m^2/L

b) 11.44m^2/L x 1000L/1m^3 = 11440m^-1 (L is the SI unit for volume)

c) I originally did 1/466 to get the inverse of 466ft^2/gal to get 0.002 gal/ft^2 but this is WRONG.

Any help on part C would be very much appreciated!
 
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I don't see how .002 gal/ft^2 is wrong. Could they mean in liters/meter^2 ?
 
phinds said:
I don't see how .002 gal/ft^2 is wrong. Could they mean in liters/meter^2 ?

I didn't understand this either. In this example, the units were given so I know gal/ft^2 is correct.

Thanks for your help!
 
It's probably considered wrong because 466 has 3 significant digits, whereas 0.002 only has one.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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