Pregunta
Use dimensional analysis to convert the quantity to the indicated units. 12 inches (in.) \( =1 \) foot 3ft to yd 3 feet \( =1 \) yard 36 inches \( =1 \) yard 5280 feef \( =1 \mathrm{mile} \) \( \square \) yd (Round to the nearest hundredth as needed.)
Ask by Olson Bush. in the United States
Mar 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
3 feet is equal to 1.00 yards.
Solución
To convert 3 feet to yards using dimensional analysis, we will use the known conversion factors provided.
1. **Identify the known conversion factors:**
- \( 3 \text{ ft} = 1 \text{ yd} \)
2. **Set up the conversion:**
We want to convert feet to yards. We can use the conversion factor directly:
\[
\text{yards} = \text{feet} \times \left( \frac{\text{yards}}{\text{feet}} \right)
\]
3. **Substituting the values:**
\[
\text{yards} = 3 \text{ ft} \times \left( \frac{1 \text{ yd}}{3 \text{ ft}} \right)
\]
4. **Perform the calculation:**
\[
\text{yards} = 3 \times \frac{1}{3} = 1 \text{ yd}
\]
Thus, \( 3 \text{ ft} = 1 \text{ yd} \).
Now, rounding to the nearest hundredth, we still have:
\[
\text{yards} = 1.00 \text{ yd}
\]
Therefore, the final answer is:
\[
\boxed{1.00} \text{ yd}
\]
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Bonus Knowledge
To convert 3 feet to yards, you can set up the dimensional analysis as follows: 1. Start with your initial quantity: \( 3 \, \text{ft} \). 2. Use the conversion factor \( 1 \, \text{yd} = 3 \, \text{ft} \) to convert feet to yards: \[ 3 \, \text{ft} \times \frac{1 \, \text{yd}}{3 \, \text{ft}} = 1 \, \text{yd} \] So, \( 3 \, \text{ft} = 1 \, \text{yd} \) exactly. If you're rounding to the nearest hundredth, the answer remains \( 1.00 \, \text{yd} \). Now you've successfully converted feet to yards using dimensional analysis!

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