Answer :
To convert 101 pounds to kilograms using dimensional analysis, you want to use a process that involves multiplying by a conversion factor. Here's a step-by-step explanation:
1. Identify the Conversion Factor:
- You know that 1 kilogram is approximately equal to 2.20462 pounds. Thus, to find out how many kilograms are in a pound, you would take the reciprocal of the value in pounds per kilogram, which is [tex]\( \frac{1 \text{ kg}}{2.20462 \text{ lbs}} \)[/tex].
2. Set Up the Conversion:
- You want to convert pounds to kilograms. Start with the given amount in pounds, which is 101 pounds.
3. Use a Unit Fraction for Conversion:
- According to the dimensional analysis method, you would set up a fraction (called a unit fraction) that allows you to cancel out the original unit (pounds) and introduce the new unit (kilograms).
- Your conversion fraction will have kilograms in the numerator and pounds in the denominator: [tex]\( \frac{1 \text{ kg}}{2.20462 \text{ lbs}} \)[/tex].
4. Perform the Multiplication:
- Multiply the number of pounds by the unit fraction:
[tex]\[
101 \text{ lbs} \times \frac{1 \text{ kg}}{2.20462 \text{ lbs}}
\][/tex]
- When you do this multiplication, the pounds unit will cancel out, and you'll be left with kilograms as your unit.
5. Choose the Correct Answer:
- From the options given, the correct choice would be:
- B. To convert pounds to kilograms, use a unit fraction with kilograms in the numerator and pounds in the denominator.
This method ensures that the conversion is done correctly, turning 101 pounds into kilograms through dimensional analysis.
1. Identify the Conversion Factor:
- You know that 1 kilogram is approximately equal to 2.20462 pounds. Thus, to find out how many kilograms are in a pound, you would take the reciprocal of the value in pounds per kilogram, which is [tex]\( \frac{1 \text{ kg}}{2.20462 \text{ lbs}} \)[/tex].
2. Set Up the Conversion:
- You want to convert pounds to kilograms. Start with the given amount in pounds, which is 101 pounds.
3. Use a Unit Fraction for Conversion:
- According to the dimensional analysis method, you would set up a fraction (called a unit fraction) that allows you to cancel out the original unit (pounds) and introduce the new unit (kilograms).
- Your conversion fraction will have kilograms in the numerator and pounds in the denominator: [tex]\( \frac{1 \text{ kg}}{2.20462 \text{ lbs}} \)[/tex].
4. Perform the Multiplication:
- Multiply the number of pounds by the unit fraction:
[tex]\[
101 \text{ lbs} \times \frac{1 \text{ kg}}{2.20462 \text{ lbs}}
\][/tex]
- When you do this multiplication, the pounds unit will cancel out, and you'll be left with kilograms as your unit.
5. Choose the Correct Answer:
- From the options given, the correct choice would be:
- B. To convert pounds to kilograms, use a unit fraction with kilograms in the numerator and pounds in the denominator.
This method ensures that the conversion is done correctly, turning 101 pounds into kilograms through dimensional analysis.
