Question

question 3 of 10
how would one convert 36 yd to centimeters (2.54 cm = 1 in)?

a. $36\\,\text{yd} \times \frac{3\\,\text{ft}}{1\\,\text{yd}} \times \frac{12\\,\text{in}}{1\\,\text{ft}}$

b. $36\\,\text{yd} \times \frac{36\\,\text{in}}{1\\,\text{yd}} \times \frac{2.54\\,\text{cm}}{1\\,\text{in}}$

c. $36\\,\text{yd} \times \frac{1\\,\text{yd}}{36\\,\text{in}} \times \frac{2.54\\,\text{cm}}{1\\,\text{in}}$

d. $36\\,\text{yd} \times 3\\,\text{ft} \times 12\\,\text{in} \times 2.54\\,\text{cm}$

Explanation:

Step1: Recall unit conversion relationships

We know that 1 yard (yd) is equal to 3 feet (ft), 1 foot is equal to 12 inches (in), and 1 inch is equal to 2.54 centimeters (cm). But for the conversion from yards to centimeters, we first convert yards to inches (since we know the conversion from inches to cm: \(2.54\space cm = 1\space in\)). The correct conversion factor from yards to inches is that 1 yard has 3 feet and 1 foot has 12 inches, so \(1\space yd=3\times12 = 36\space in\). So to convert yards to inches, we use the factor \(\frac{36\space in}{1\space yd}\), and then to convert inches to cm, we use \(\frac{2.54\space cm}{1\space in}\).

Step2: Analyze each option

• Option A: This converts yards to feet to inches, but it stops at inches and doesn't convert to centimeters. So it's incomplete.
• Option B: First, \(36\space yd\times\frac{36\space in}{1\space yd}\) converts yards to inches (since \(1\space yd = 36\space in\)), then \(\times\frac{2.54\space cm}{1\space in}\) converts inches to centimeters. This is the correct sequence of unit conversions.
• Option C: The conversion factor \(\frac{1\space yd}{36\space in}\) is incorrect (it should be \(\frac{36\space in}{1\space yd}\) to convert yards to inches), so this option has a wrong conversion factor.
• Option D: This multiplies all the units together without proper unit cancellation. The units here would be \(yd\times ft\times in\times cm\), which is not a valid way to convert units as the units don't cancel out correctly.

Answer:

B. \(36\space yd\times\frac{36\space in}{1\space yd}\times\frac{2.54\space cm}{1\space in}\)