- The area of Liberia is given as \(1.1 \times 10^5 \text{ km}^2\).
- Converting the distance \(2.54 \times 10^{-1} \text{ m}\) to kilometers gives \(2.54 \times 10^{-4} \text{ km}\).
- A 300-page book consists of \(150\) leaves.
- The thickness of one leaf, given a total book thickness of \(15 \text{ mm}\), is \(1 \times 10^{-4} \text{ m}\).
- \(\boxed{1.1 \times 10^5 \text{ km}^2, 2.54 \times 10^{-4} \text{ km}, 150, 1 \times 10^{-4} \text{ m}}\)
Explanation
- Determine the Area of Liberia
To determine the area of Liberia, we refer to the provided data which states the area as \(1.1 \times 10^5 \text{ km}^2\). This is the approximate surface area of the country.
- Convert Distance to Kilometers
To express the distance \(2.54 \times 10^{-1} \text{ m}\) in kilometers, we use the conversion factor \(1 \text{ km} = 10^3 \text{ m}\), which means \(1 \text{ m} = 10^{-3} \text{ km}\).
Substituting this conversion:
\[2.54 \times 10^{-1} \text{ m} = 2.54 \times 10^{-1} \times 10^{-3} \text{ km} = 2.54 \times 10^{-4} \text{ km}.\]
The distance in kilometers in standard form is therefore \(2.54 \times 10^{-4} \text{ km}\).
- Determine the Number of Leaves in the Book
A book has pages numbered from 1 to 300. Since one leaf of paper represents 2 pages (front and back), we divide the total number of pages by 2:
\[\text{Number of leaves} = \frac{300 \text{ pages}}{2 \text{ pages/leaf}} = 150 \text{ leaves}.\]
The book contains 150 leaves.
- Calculate the Thickness of One Leaf
The total thickness of the book is \(15 \text{ mm}\). First, convert this to meters:
\[15 \text{ mm} = 15 \times 10^{-3} \text{ m} = 1.5 \times 10^{-2} \text{ m}.\]
Now, divide the total thickness by the number of leaves (150) to find the thickness of a single leaf:
\[\text{Thickness per leaf} = \frac{1.5 \times 10^{-2} \text{ m}}{150} = \frac{1.5 \times 10^{-2} \text{ m}}{1.5 \times 10^2} = \left(\frac{1.5}{1.5}\right) \times 10^{-2-2} \text{ m} = 1 \times 10^{-4} \text{ m}.\]
The thickness of one leaf is \(1 \times 10^{-4} \text{ m}\).
Examples
Understanding scientific notation and unit conversion is crucial in fields like cartography and engineering. For instance, if you are designing a miniature component, you need to precisely convert between millimeters and meters to ensure your measurements are accurate. Similarly, calculating the thickness of a single sheet of paper is a classic way to practice working with very small dimensions and standard scientific form, helping you visualize physical scales.