Unit conversions for mass: which of the following stated conversion formulas is incorrect?

Difficulty: Easy

Correct Answer: 1 tonne = 1000 kg = 22.046 lbs

Explanation:


Introduction / Context:
Accurate engineering calculations rely on correct unit conversions. Tonne, metric ton, U.S. short ton, and long (imperial) ton are frequently confused. This question asks you to identify the incorrect statement among several common mass conversions encountered in process design and supply chain calculations.


Given Data / Assumptions:

  • 1 tonne (metric ton) = 1000 kg exactly.
  • 1 kilogram = 2.20462 pounds (lbs).
  • 1 U.S. short ton = 2000 lbs ≈ 907.1847 kg ≈ 0.907 tonne.
  • 1 long ton (ton) = 2240 lbs ≈ 1016.0469 kg ≈ 1.016 tonnes.


Concept / Approach:
Convert the tonne to pounds using 1 kg = 2.20462 lbs. Then validate the other conversions. The first statement incorrectly lists 22.046 lbs for a tonne, which is short by a factor of 100. Correct is approximately 2204.6 lbs. The other statements align with standard references within rounding tolerance.


Step-by-Step Solution:
Compute pounds per tonne: 1000 kg * 2.20462 lbs kg^-1 ≈ 2204.62 lbs.Compare with the given value 22.046 lbs → incorrect by two orders of magnitude.Validate short ton: 2000 lbs ≈ 907 kg → 0.907 tonne and ≈ 0.893 of a long ton (2000/2240).Validate long ton: 2240 lbs ≈ 1016 kg ≈ 1.016 tonnes and 2240/2000 = 1.12 U.S. tons.


Verification / Alternative check:
Cross check with any reputable unit-conversion table or dimensional analysis tool to confirm the numeric factors.


Why Other Options Are Wrong:
They are actually correct within normal engineering rounding, so they are not the incorrect formulas.


Common Pitfalls:
Dropping zeros in conversions; mixing mass (tonne) and force (ton-force); confusing long and short ton definitions.


Final Answer:
1 tonne = 1000 kg = 22.046 lbs

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