Fun with Numbers

I filled up the new Tardis' gas tank today. 12.695 gallons. How big is this tank anyway?

One of the fancy button features on this new car is its estimation of how many miles can be driven on the available gas. Watching this number defies my simple understanding of math.

After I filled up the tank and started the car, the message window said "400 miles to empty tank." By the time I got home, .2 miles later, the message said "395 miles to empty tank." When I restarted the car a few hours later, it had reconsidered this number to "400 miles to empty tank." By the time I parked at the grocery store, 3.9 miles later, the message had changed to "405 miles to empty tank." Then, when I reached school, another 2.6 miles, I had "385 miles to empty tank." By the time I was back home, another 2.5 miles, the car was saying "380 miles to empty tank."

So, in 9.2 miles I lost 20 miles of gas.

Just to make the numbers clearer, during this same loop around town, the "instantaneous" mileage ranged from 4.3 mpg to 99.9 mpg.

Fortunately there is a normal gas tank gage with a little needle that swings from Full to Empty, and so far appears to operate in a linear fashion. If it is almost to the red line, better fill her up soon.