Goal
Convert 155 lbs to kilograms using dimensional analysis (unit cancellation). In classical mechanics, “lb” can refer to pounds-force (a force) or pound-mass (a mass); here lb is interpreted as pound-mass, which is the standard intent of “lbs to kg”.
Step 1: Use the correct conversion factor
The SI unit of mass is the kilogram (kg). The pound-mass is related to kilograms by the exact definition: \[ 1\ \text{lb} = 0.45359237\ \text{kg} \]
Step 2: Set up dimensional analysis (units cancel)
Multiply by a ratio equal to 1, choosing the arrangement so that lb cancels: \[ 155\ \text{lb} \times \frac{0.45359237\ \text{kg}}{1\ \text{lb}} \]
The lb unit appears in both numerator and denominator, so it cancels, leaving kilograms.
Step 3: Perform the calculation
\[ 155 \times 0.45359237 = 70.30681735 \] \[ 155\ \text{lb} = 70.30681735\ \text{kg} \]
Step 4: Round using significant figures
The given value 155 has three significant figures. The conversion factor is exact, so the result is reported to three significant figures: \[ 70.30681735\ \text{kg} \approx 70.3\ \text{kg} \]
Final result: 155 lbs to kg gives \(70.3\ \text{kg}\) (3 significant figures).
Quick check (sanity check)
Since \(1\ \text{kg} \approx 2.20462\ \text{lb}\), converting back should return approximately 155 lb: \[ 70.30681735\ \text{kg} \times 2.20462\ \frac{\text{lb}}{\text{kg}} \approx 155\ \text{lb} \]
Visualization: conversion flow with unit cancellation
Optional mechanics note: mass vs weight
In classical mechanics, weight is a force \(W\) related to mass \(m\) by \(W = m g\). If the mass is \(m = 70.30681735\ \text{kg}\) and \(g = 9.80665\ \text{m/s}^2\), then: \[ W = 70.30681735 \times 9.80665 \approx 689.4743504\ \text{N} \]