Question

The longest river in the world is the Nile River with a length of 4145 mi. How long is the Nile in cable lengths, meters, and nautical miles? Use these exact conversions to help solve the problem: $$\begin{aligned} 6 \mathrm{ft} &=1 \text { fathom } \\ 100 \mathrm{fathoms} &=1 \text { cable length } \\ 10 \text { cable lengths } &=1 \text { nautical mile } \\ 3 \text { nautical miles } &=1 \text { league } \end{aligned}$$

Short answer

In summary, the Nile River is approximately 36,476 cable lengths, 3,647.6 nautical miles, and 1,995,234.91 meters long.

Step-by-step solution

Convert miles to fathoms

To convert the length of the Nile River from miles to fathoms, we need to use the following conversion: 1 mile = 880 fathoms Now, we can calculate the length of the Nile in fathoms by multiplying its length in miles by the conversion factor: \(Length_{fathoms} = Length_{miles} × Conversion\_factor\) \(Length_{fathoms} = 4145 × 880 \)

Calculate the length in fathoms

Now let's multiply the length in miles by the conversion factor to get the length in fathoms: \(Length_{fathoms} = 4145 × 880 = 3647600 \text{ fathoms}\) The length of the Nile River is equal to 3,647,600 fathoms.

Convert fathoms to cable lengths, nautical miles, and meters

Now that we have the length in fathoms, we can use the given conversions to find the length in cable lengths, nautical miles, and meters: 1 cable length = 100 fathoms 1 nautical mile = 10 cable lengths 1 meter = 1.8288 fathoms (approximately) To convert fathoms to cable lengths, nautical miles, and meters, we'll use the following formulas: \(Length_{cable\_lengths} = \frac{Length_{fathoms}}{100}\) \(Length_{nautical\_miles} = \frac{Length_{fathoms}}{100 × 10}\) \(Length_{meters} = \frac{Length_{fathoms}}{1.8288}\)

Calculate the length in cable lengths, nautical miles, and meters

Now, let's use the formulas from Step 3 to find the length of the Nile River in cable lengths, nautical miles, and meters: \(Length_{cable\_lengths} = \frac{3647600}{100} = 36476 \text{ cable lengths}\) \(Length_{nautical\_miles} = \frac{3647600}{100 × 10} = 3647.6 \text{ nautical miles}\) \(Length_{meters} = \frac{3647600}{1.8288} ≈ 1995234.91 \text{ meters}\) So, the length of the Nile River is approximately: - 36,476 cable lengths - 3,647.6 nautical miles - 1,995,234.91 meters

Key concepts

Length Measurement

Length measurement is an important aspect of understanding the world around us. We often use different units to describe length, depending on the context. For instance, in everyday situations, we use inches, feet, and miles in the United States. However, other measurement systems, like the metric system, use millimeters, centimeters, and meters.
Understanding how different units of length relate to each other is crucial. This skill allows us to convert between systems or within the same system. For instance, if you know how many feet are in a mile, you can convert miles to feet easily. Similarly, learning about other units like fathoms, cable lengths, and nautical miles can also be useful, especially when dealing with nautical measurements.
To aid in these conversions, we rely on conversion factors, which are multipliers that allow us to move from one unit to another. Using conversion factors systematically is key to mastering length measurements, especially when dealing with unusual units or when working in fields like navigation or maritime studies.

Nautical Units

Nautical units are specialized units of length used primarily in maritime and aviation contexts. These units are directly linked to the Earth's geography and are especially important for navigation. The nautical mile, for example, is based on the Earth's circumference and is equal to one minute of latitude.

• Fathom: A unit used for measuring the depth of water. One fathom is equal to 6 feet.
• Cable Length: This unit is useful for sea distances and equals 100 fathoms.
• Nautical Mile: Equal to 10 cable lengths or about 1.15078 regular miles. It considers the curvature of the Earth, making it useful for navigation across oceans and long distances.
• League: Though not commonly used, a league is equal to 3 nautical miles.

These units are interconnected by precise conversion factors, making it essential to understand them when solving problems related to sea travel or navigation. Mariners, for instance, often convert between these units to calculate distances traveled and navigational positioning accurately.

Metric System

The metric system is an internationally accepted system of measurement used by most countries around the world. It's known for its simplicity and ease of use, as it is based on powers of ten, making calculations straightforward.

• Base Unit: The meter is the basic unit of length in the metric system.
• Kilo Prefix: Kilometer, where "kilo" indicates a thousand, signifies 1000 meters.
• Milli and Centi Prefixes: Millimeter and centimeter denote one-thousandth and one-hundredth of a meter, respectively.

Converting between units in the metric system is simply a matter of moving the decimal point. For example, to convert 1000 millimeters to meters, you divide by 1000, giving you 1 meter. The metric system's ease of conversion and consistency makes it an excellent tool for scientific, educational, and everyday purposes. Furthermore, understanding how to convert measurements from other systems to metric can be extremely useful, especially when working with global contexts or scientific data.