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broken reciprocal unit conversion from mpg to L/100 km

Posted 10 years ago

My US rental car displays an average fuel economy of 33.2 mpg. I would like WA to convert this to the Australian standard of fuel consumption in L/100km. Try "33.2 mpg in L/100km" This conversion has been broken since Day 1 of WA. Am I missing something?

POSTED BY: Adam Tester
6 Replies

Am I missing something?

Yes, of course. Miles (a length unit) per gallons (a volume unit) should convert into 100 km (a length unit) per Liter (a volume unit). Doing so

33.2 mpg in 100km/L

the input interpretation is: convert 33.2 mpg (miles per galon) to kilometers per liter

and Wolfram|Alpha answers that by

14.11 km/L

or 0.01411 (100 km)/L

The input interpretation given by Wolfram|Alpha is not for Wolfram|Alpha, but for the problem owner.

POSTED BY: Udo Krause
Posted 10 years ago

Thanks Udo, I understand dimensional similarity. However, as I pointed out above, WA is smart enough to perform some reciprocal unit conversions. Try "33 mpg in L/km"

POSTED BY: Adam Tester

Of course, when querying for 33.2 mpg, Wolfram|Alpha tells us among other things that this corresponds to 7.1 L/100 km. enter image description here

POSTED BY: Ilian Gachevski
Posted 10 years ago

Thanks Ilian, it's an interesting way to input the problem.

POSTED BY: Adam Tester

There are two things preventing this from happening that I see:

  • 100km isn't recognized as a unit by itself
  • MPG and L/100km are inverses of each other and not the same dimensions

So the unit converter won't handle these kinds of queries naturally. This sounds like a great suggestion for how Wolfram|Alpha can be improved.

If you ever see anything that can improved like this, let the Wolfram|Alpha team know in the feedback form at the bottom of the query page next to "Give us your feedback":

http://www.wolframalpha.com/input/?i=2+100km

POSTED BY: Sean Clarke
Posted 10 years ago

Thanks Sean, but I don't agree with your analysis: 1. Firstly, WA DOES understand reciprocal unit conversions, try "33 mpg in L/km". Neat! 2.. I know "100 km" is not a desirable way of writing a unit, but it is widely used and legislated in Europe and Australia for fuel consumption.

In my analysis, the error occurs because of incorrect operator precedence: WA divides "33 mpg in L" by "100km", which is meaningless. I can't guess why WA behaves correctly with the similar expression "33 mpg in L/km". If WA adopted the following operator precedence, it could parse factor-units like "100km" : 1. prefix-unit (e.g. km). 2. exponentiation (e.g. km^2) 3. factor-unit (e.g. 100 km^2) 4. left-to-right division and multiplication 5. left-to-right addition and subtraction

POSTED BY: Adam Tester
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