Long ton is defined exactly as 2240 lb. What is this mass in kilograms?
The Correct Answer and Explanation is:
Correct Answer: 1016.05 kg
To solve this problem, you need to convert a mass given in pounds (lb) to its equivalent in kilograms (kg). The question specifies that a long ton is exactly 2240 lb. This requires using the standard conversion factor between the imperial unit of pounds and the SI unit of kilograms.
The internationally accepted conversion factor is that 1 kilogram is equivalent to approximately 2.20462 pounds. For a more direct calculation, it is often easier to use the factor that 1 pound is exactly equal to 0.45359237 kilograms. Since the problem gives the initial value in pounds, using this second factor allows for a straightforward multiplication.
The method for this conversion is called dimensional analysis. You start with the value you want to convert and multiply it by a conversion factor written as a fraction. The fraction is arranged so that the original units cancel out, leaving you with the desired units.
Here is the setup for the calculation:
Mass in kg = 2240 lb × (0.45359237 kg / 1 lb)
In this setup, the “lb” unit in the numerator (from 2240 lb) cancels out with the “lb” unit in the denominator of the fraction, leaving only “kg” as the final unit.
Now, perform the multiplication:
2240 × 0.45359237 = 1016.0469088 kg
For most practical purposes, rounding the answer to two decimal places is sufficient. Therefore, the mass of a long ton in kilograms is approximately 1016.05 kg.
It is important to distinguish the long ton (2240 lb) from other units. The short ton, common in the United States, is 2000 lb. The metric tonne is defined as exactly 1000 kg. The incorrect answer of 1000 kg provided in the image likely resulted from confusing the long ton with the metric tonne.
