Litres per 100 km and miles per gallon are reciprocal, not proportional: mpg = 235.215 ÷ (l/100 km). One measures how much fuel a distance costs, the other how much distance a fuel amount buys, and no single multiplier converts between them.
About the units
The two conventions describe the same physical thing from opposite ends. Consumption units — litres per 100 kilometres, used across Europe — put fuel in the numerator, so a lower number is better and the scale is linear in fuel. Efficiency units — miles per gallon, used in the United States and Britain — put distance in the numerator, so a higher number is better and the scale is linear in distance. The reciprocal relationship has a real consequence: improvements at the thirsty end of the mpg scale save far more fuel than the same numerical improvement at the efficient end.
The exact factor
The constant is 235.21458333, derived from 100 km expressed in miles (62.137119) multiplied by the litres in a US gallon (3.785411784), then inverted appropriately. So 8 l/100 km is 29.4 mpg, and 30 mpg is 7.84 l/100 km. The reciprocal trap is worth spelling out: going from 15 to 20 mpg saves 1.67 gallons per 100 miles, while going from 40 to 45 mpg saves only 0.28 — three times less fuel for the same five-mpg gain. That is why fleet regulations and carbon accounting use consumption units, and why the US EPA now prints gallons per 100 miles alongside mpg.
Where you meet this conversion
Comparing European and American vehicle data, which is the whole reason this page exists. A car sold in both markets carries both figures, and journalists converting between them by multiplying get nonsense. Fleet fuel budgeting, carbon reporting and eco-driving all work better in consumption units for the reason above. Note that American mpg uses the US gallon while British mpg uses the imperial one, so there are two different mpg scales — see the separate pages for each.