Explain how to use the unit-factor method to convert 120 pounds to kilograms.
The Correct Answer and Explanation is:
To convert 120 pounds to kilograms using the unit-factor method, you follow these steps:
Step 1: Know the conversion factor
1 pound (lb) is approximately equal to 0.4536 kilograms (kg).
Step 2: Set up the conversion using a unit fraction
Write the given amount as a fraction:
120 lb / 1
Then multiply by the conversion factor written as a fraction so the pounds unit cancels out:
(0.4536 kg / 1 lb)
Step 3: Multiply and cancel units
120 lb×(0.4536 kg1 lb)=54.432 kg120 \, \text{lb} \times \left( \frac{0.4536 \, \text{kg}}{1 \, \text{lb}} \right) = 54.432 \, \text{kg}120lb×(1lb0.4536kg)=54.432kg
The pounds units cancel, leaving the answer in kilograms.
Final Answer:
120 pounds = 54.432 kilograms
Explanation
The unit-factor method is a technique used in dimensional analysis that allows for the conversion between units by multiplying by a fraction that equals one. This fraction, called a unit factor, is derived from an equivalency statement between two units. In this case, the equivalency is:
1 pound = 0.4536 kilograms
We begin by expressing the quantity we want to convert, which is 120 pounds, as a fraction over one. Then, we multiply this by the unit factor. It is essential to arrange the unit factor so the unit we want to cancel, pounds, appears in the denominator. The desired unit, kilograms, must be in the numerator.
Multiplying the values together and canceling out the common units ensures a clean and accurate conversion. After multiplying 120 by 0.4536, we get 54.432 kilograms.
This method works for all types of unit conversions—mass, volume, length, and more—provided that a correct and precise conversion factor is used. Always double-check the placement of units in the unit factor to ensure the unwanted units cancel and the result is in the correct final unit. The unit-factor method is reliable, especially when dealing with complex or multi-step conversions, because it makes the cancellation process clear and helps prevent unit errors.
