How to convert pressure units from Pascals to Pound per Square Inch?

Question

My Physics Teacher wanted us to convert Pascal into Pound per Square Inch, not psi... he mentioned we'd use 9.8 m/s²... I'm not sure. I already did the simplest but it's not quite the answer: I used the unit psi 'cause I figured it's the same as pound per square inch (where I divided 1 lb/in² by 6894.75727 Pascals and multiply the quotient by the given Pascal unit which is 300) ... Our teacher must've required us to show the correct cancellations of units and the division plus multiplication, of course, to come up with the unit pound per square inch (lb/in²). The problem is, to avoid confusion, 300 Pa to lb/in².

Answer 1

$$ 1~\text{Pa} = 1~\frac{\text{N}}{\text{m}^2} = 0.2248~\frac{\text{lbf}}{\text{m}^2} $$ because $1~\text{N} \approx 0.2248$ pounds-force. Then $$ 0.2248~\frac{\text{lbf}}{\text{m}^2}=0.2248~\frac{\text{lbf}}{(1~\text{m})^2} = 0.2248~\frac{\text{lbf}}{\left(39.37~\text{in} \right)^2} \approx 1.4503 \cdot 10^{-4}~\frac{\text{lbf}}{\text{in}^2} $$ therefore, $1~\text{Pa} \approx 1.4503 \cdot 10^{-4}~\text{psi}$. In order to get $300~\text{Pa}$, multiply both sides by $300$.

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And what about the converting from Newton to pounds-force? We know that $$ 1~\text{lb} = 0.4536~\text{kg} \Rightarrow 1~\text{lbf} = 9.81~\frac{\text{m}}{\text{s}^2} \cdot 0.4536~\text{kg} \approx 4.448~\frac{\text{kg}\cdot \text{m}}{\text{s}^2} = 4.448~\text{N} $$ and therefore $$ 1~\text{lbf} = 4.448~\text{N}  \Rightarrow 1~\text{N} = \frac{1}{4.448}~\text{lbf} \approx 0.2248 ~\text{lbf} $$ Is it clear now?