The formula with 4.5 substituted
US gallons = 4.5 ÷ 3.785411784 = 1.189
The constant is an exact definition, not a rounded factor: the mile is 1.609344 km, the US gallon is 3.785411784 litres and the imperial gallon is 4.54609 litres. The Litres to Gallons Converter explains where each comes from and gives a longer table.
4.5 litres is 1.189 US gallons and 0.990 imperial gallons. The imperial gallon is 4.54609 litres against the US gallon's 3.785411784, which is why the two answers differ by a fifth.
What 4.5 litres means in practice
4.5 litres is 1.189 US gallons and 0.990 imperial gallons, which is to say almost exactly one imperial gallon: the true imperial gallon is 4.54609 litres. That coincidence is why British readers remember the gallon as 'four and a half litres'.