A typical dollar bill is 15.50 cm by 6.50 cm.Calculate the surface area in square meters, square centimeters and square nanometers.

Step 1: 
Calculate the surface area in square centimeters: 
\[\text { Area} = 15.50 \space \text { cm} \times 6.50 \space \text { cm} = 100.75 \space \text { cm} ^ 2\]

Step 2:

Convert square centimeters to square meters: 
\[1 \space \text { cm} ^ 2 = 0.0001 \space \text { m} ^ 2\]
\[100.75 \space \text { cm} ^ 2 \times 0.0001 \space \text { m} ^ 2/\text { cm} ^ 2 = 0.010075 \space \text { m} ^ 2\]

Step 3:

Convert square centimeters to square nanometers: 
\[1 \space \text { cm} ^ 2 = 10^ { 14} \space \text { nm} ^ 2\]
\[100.75 \space \text { cm} ^ 2 \times 10^ { 14} \space \text { nm} ^ 2/\text { cm} ^ 2 = 1.0075 \times 10^ { 16} \space \text { nm} ^ 2\]

Supplemental Knowledge:

Calculating the surface area of a rectangle involves multiplying its length by its width. When converting between different units of area, it's important to remember the conversion factors:

1. Square Centimeters to Square Meters: 
\(1 \text { square meter} = 10,000 \text { square centimeters} \) 
\(1 \text { square centimeter} = 0.0001 \text { square meters} \)

2. Square Centimeters to Square Nanometers: 
\(1 \text { centimeter} = 10^ 7 \text { nanometers} \) 
\(1 \text { square centimeter} = ( 10^ 7) ^ 2 = 10^ { 14} \text { square nanometers} \)

From Concepts to Reality:

Understanding how to calculate and convert surface areas can be useful in various scenarios:

- Interior Design: 
When planning to cover surfaces with materials like wallpaper or paint, knowing how to calculate and convert surface areas ensures you purchase the correct amount of materials.

- Manufacturing: 
In industries where precise measurements are crucial (e.g., electronics manufacturing), converting between units like centimeters and nanometers helps maintain accuracy in product specifications.

Mastering unit conversions and surface area calculations can greatly enhance your problem-solving skills in both academic and real-world contexts. At UpStudy, we provide tools and resources designed to help you excel in mathematics and beyond.

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