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How would one convert 36 yd to centimeters ([tex]\(2.54 \text{ cm} = 1 \text{ in}\)[/tex])?

A. [tex]\(36 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}}\)[/tex]

B. [tex]\(36 \text{ yd} \times 3 \text{ ft} \times 12 \text{ in} \times 2.54 \text{ cm}\)[/tex]

C. [tex]\(36 \text{ yd} \times \frac{36 \text{ in}}{1 \text{ yd}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\)[/tex]

D. [tex]\(36 \text{ yd} \times \frac{1 \text{ yd}}{36 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\)[/tex]

Sagot :

GinnyAnswer
To convert 36 yards to centimeters, we'll go through the conversion steps one by one.

### Step 1: Convert Yards to Feet
First, we need to convert the length from yards to feet. We know that:
[tex]\[ 1 \text{ yard} = 3 \text{ feet} \][/tex]

For 36 yards:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} = 108 \text{ feet} \][/tex]

### Step 2: Convert Feet to Inches
Next, we convert the feet to inches. We know that:
[tex]\[ 1 \text{ foot} = 12 \text{ inches} \][/tex]

For 108 feet:
[tex]\[ 108 \text{ feet} \times 12 \text{ inches per foot} = 1296 \text{ inches} \][/tex]

### Step 3: Convert Inches to Centimeters
Finally, we convert the length from inches to centimeters. We know that:
[tex]\[ 1 \text{ inch} = 2.54 \text{ centimeters} \][/tex]

For 1296 inches:
[tex]\[ 1296 \text{ inches} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]

### Summary of Conversion Steps
Combining these steps, we get:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} \times 12 \text{ inches per foot} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]

This matches the calculation done step-by-step earlier and confirms that the conversion process is correct.

### Identifying the Correct Choice
Given the steps and how they align with the multiple choices provided:
- Option A:

[tex]\[36 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}}\][/tex]

This part correctly converts yards to inches but does not go to centimeters.

- Option B:

[tex]\[36 \text{ yd} \times 3 \text{ ft} \times 12 \text{ in} \times 2.54 \text{ cm}\][/tex]

This choice correctly includes all necessary conversion factors for converting yards to centimeters.

- Option C:

[tex]\[36 \text{ yd} \times \frac{36 \text{ in}}{1 \text{ yd}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]

This incorrectly multiplies the yard by 36 instead of converting foot-inches first.

- Option D:

[tex]\[36 \text{ yd} \times \frac{1 \text{ yd}}{36 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]

This incorrectly attempts to invert the ratio and would give an incorrect conversion.

Thus, the correct selection method from the choices given is [tex]\( \boxed{B} \)[/tex].
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