To convert 205 U.S. pounds (lb) into grams (g) using dimensional analysis, we follow these steps:
### Step 1: Convert Pounds to Kilograms
We know that 1 kilogram (kg) is equivalent to 2.2 pounds (lb). This can be written as the conversion factor:
[tex]\[ 1 \, \text{kg} = 2.2 \, \text{lb} \][/tex]
We need to find how many kilograms 205 pounds are. To do this, we use the conversion factor by dividing 205 pounds by 2.2 pounds per kilogram:
[tex]\[ \text{kilograms} = \frac{205 \, \text{lb}}{2.2 \, \text{lb/kg}} \][/tex]
This yields:
[tex]\[ \text{kilograms} = 93.18 \, \text{kg} \][/tex]
### Step 2: Convert Kilograms to Grams
Next, we need to convert kilograms to grams. We know that:
[tex]\[ 1 \, \text{kg} = 1000 \, \text{g} \][/tex]
So, we multiply the number of kilograms we obtained by 1000 to convert it to grams:
[tex]\[ \text{grams} = 93.18 \, \text{kg} \times 1000 \, \text{g/kg} \][/tex]
This gives us:
[tex]\[ \text{grams} = 93181.82 \, \text{g} \][/tex]
### Rounding
Finally, we need to round the answer to 2 decimal places. In this case, the number 93181.82 is already rounded to 2 decimal places, so no further rounding is necessary.
Therefore, 205 U.S. pounds is equivalent to 93181.82 grams.
