Question
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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

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Tutor-Verified Answer

Answer

3 feet is equal to 1.00 yards.

Solution

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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