17) The following exact conversion equivalents are given: 1 m = 100 cm , 1 in = 2.54 cm, and 1 ft 12 in. If a computer screen has an area of 1.27 ft2, this area is closest to (Show work). A) 0.00284 m2. B) 0.0465 m2. C) 0.118 m2. D) 0.284 m2. E) 4.65 m2.

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem 17: Area Conversion**

The following exact conversion equivalents are given: 
- 1 meter (m) = 100 centimeters (cm)
- 1 inch (in) = 2.54 centimeters (cm)
- 1 foot (ft) = 12 inches (in)

**Question:**
If a computer screen has an area of 1.27 square feet (ft²), this area is closest to which of the following values? *(Show work)*

**Options:**
A) 0.00284 square meters (m²)  
B) 0.0465 square meters (m²)  
C) 0.118 square meters (m²)  
D) 0.284 square meters (m²)  
E) 4.65 square meters (m²)  

**Detailed Solution Explanation:**

To convert from square feet (ft²) to square meters (m²), follow these steps:

1. **Convert feet to inches**:
   - Since 1 ft = 12 in, an area of 1.27 ft² can be seen as the area occupied by a square with a side length equivalent to the square root of 1.27 feet, all sides being of equal length.

2. **Convert inches to centimeters**:
   - Since 1 in = 2.54 cm, find the equivalent area in cm².

3. **Convert centimeters to meters**:
   - Since 1 m = 100 cm, further convert the area from cm² to m².

This step-by-step conversion approach ensures the correct conversion from ft² to m² for accurately determining the area in square meters.
Transcribed Image Text:**Problem 17: Area Conversion** The following exact conversion equivalents are given: - 1 meter (m) = 100 centimeters (cm) - 1 inch (in) = 2.54 centimeters (cm) - 1 foot (ft) = 12 inches (in) **Question:** If a computer screen has an area of 1.27 square feet (ft²), this area is closest to which of the following values? *(Show work)* **Options:** A) 0.00284 square meters (m²) B) 0.0465 square meters (m²) C) 0.118 square meters (m²) D) 0.284 square meters (m²) E) 4.65 square meters (m²) **Detailed Solution Explanation:** To convert from square feet (ft²) to square meters (m²), follow these steps: 1. **Convert feet to inches**: - Since 1 ft = 12 in, an area of 1.27 ft² can be seen as the area occupied by a square with a side length equivalent to the square root of 1.27 feet, all sides being of equal length. 2. **Convert inches to centimeters**: - Since 1 in = 2.54 cm, find the equivalent area in cm². 3. **Convert centimeters to meters**: - Since 1 m = 100 cm, further convert the area from cm² to m². This step-by-step conversion approach ensures the correct conversion from ft² to m² for accurately determining the area in square meters.
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