378.541l = 100USgal.
This would be easier in traditional units.
To answer your question, yes, multiply the pulses per hour by 378.541l/pulse to get l/h.
TL;DR
if this equation
is true, then we can divide both sides of that equation by [1 pulse]:
Code:
1 pulse 378.541 litre
------- = -------------
1 pulse 1 pulse
Since quantity divided by itself is 1, the left-hand side reduces to 1:
Code:
378.541 litre litre
1 = ------- ----- = 378.541 -----
1 pulse pulse
So that means that, in the context of that flowmeter, the quantity [378.541 litre/pulse] equals 1.
Since multiplication by 1 is the multiplicative identity operation, we can multiply an initial quantity by 1 and the result is equal to the initial quantity.
pulse
1000 -----
hour
pulse
= 1000 ----- * 1
hour
pulse litre
= 1000 ----- * 378.541 -----
hour pulse
litre
= 1000 * 378.541 -----
hour
litre
= 378,541 -----
hour
To summarize, we are not multiplying by 378.541, we are multiplying by unity i.e. by one. In my experience, 80-90% of practical engineering boils down to multiplying by unity, and the only hard part is determining the context-dependent, applicable value of unity.
Kudos to you for intuitively figuring out the right answer; harsh criticism to your past teachers and mentors that this was not taught to the point that you knew it in your bones and didn't have to ask the question in the first place.
Nevertheless, welcome to the forum.