If a person weighs 133 lbs and is 5’2″ tall, what is their height in meters and weight (mass) in kg? Show work using dimensional analysis and give answers with correct sig figs and units. Calculation of height in meters (m): To convert feet to meters, we use the conversion factor 1 ft = 0.3048 m. 5 ft * 0.3048 m/ft = 1.524 m To convert inches to meters, we use the conversion factor 1 in = 0.0254 m. 2 in * 0.0254 m/in = 0.0508 m Total height in meters = 1.524 m + 0.0508 m = 1.5748 m (rounded to 4 sig figs) Calculation of weight (mass) in kilograms (kg): To convert pounds to kilograms, we use the conversion factor 1 lb = 0.453592 kg. 133 lb * 0.453592 kg/lb = 60.327596 kg (rounded to 4 sig figs)
The Correct Answer and Explanation is:
Correct Answer:
- Height in meters: 1.574 m
- Weight (mass) in kilograms: 60.33 kg
Explanation
To accurately convert height and weight into metric units, dimensional analysis is applied using appropriate conversion factors. This method ensures consistency in units and minimizes error.
For height, the individual stands at 5 feet 2 inches. First, the conversion from feet to meters uses the factor 1 foot = 0.3048 meters. Multiplying 5 feet by this factor gives:
5 ft×0.3048 m1 ft=1.524 m5\ \text{ft} \times \frac{0.3048\ \text{m}}{1\ \text{ft}} = 1.524\ \text{m}5 ft×1 ft0.3048 m=1.524 m
Next, convert the 2 inches into meters using the factor 1 inch = 0.0254 meters:
2 in×0.0254 m1 in=0.0508 m2\ \text{in} \times \frac{0.0254\ \text{m}}{1\ \text{in}} = 0.0508\ \text{m}2 in×1 in0.0254 m=0.0508 m
Adding both values provides the total height:
1.524 m+0.0508 m=1.5748 m1.524\ \text{m} + 0.0508\ \text{m} = 1.5748\ \text{m}1.524 m+0.0508 m=1.5748 m
For appropriate significant figures, the height is expressed to four significant digits as 1.574 m.
To convert weight, start with 133 pounds. Using the conversion factor 1 pound = 0.453592 kilograms:
133 lb×0.453592 kg1 lb=60.327596 kg133\ \text{lb} \times \frac{0.453592\ \text{kg}}{1\ \text{lb}} = 60.327596\ \text{kg}133 lb×1 lb0.453592 kg=60.327596 kg
Rounding this to four significant figures gives 60.33 kg. This maintains consistency with the input precision, as 133 pounds contains three significant digits, but due to the precise conversion factor, four-digit accuracy is acceptable for scientific reporting.
The dimensional analysis process eliminates unit mismatch and preserves measurement accuracy. Each calculation is structured to cancel original units while introducing the desired metric units. Careful rounding based on significant figures preserves measurement precision and reflects proper scientific practice.
