Question

You decide to go sailing in the tropics with some friends. Once there, you listen to the marine forecast, which predicts in-shore wave heights of \(1.5 \mathrm{~m}\), offshore wave heights of \(4 \mathrm{~m}\), and temperature of \(27^{\circ} \mathrm{C}\). Your friend the captain is unfamiliar with the metric system, and he needs to know whether it is safe for your small boat and if it will be warm. He asks you to convert the measurements to feet and degrees Fahrenheit, respectively.

Short answer

Wave heights: in-shore is 4.92 ft, offshore is 13.12 ft. Temperature: 80.6°F.

Step-by-step solution

Convert in-shore wave height to feet

To convert meters to feet, use the conversion factor: 1 meter = 3.28084 feet. Given: in-shore wave height = 1.5 meters.Formula: \[ \text{in-shore wave height in feet} = 1.5 \times 3.28084 \]Calculation: \[ 1.5 \times 3.28084 \text{ feet} = 4.92126 \text{ feet}\]Thus, the in-shore wave height in feet is 4.92126 feet.

Convert offshore wave height to feet

Using the same conversion factor: 1 meter = 3.28084 feet. Given: offshore wave height = 4 meters.Formula: \[ \text{offshore wave height in feet} = 4 \times 3.28084 \]Calculation: \[ 4 \times 3.28084 \text{ feet} = 13.12336 \text{ feet}\]Thus, the offshore wave height in feet is 13.12336 feet.

Convert temperature to degrees Fahrenheit

To convert Celsius to Fahrenheit, use the formula: \[ \text{Temperature in Fahrenheit} = \frac{9}{5} \times \text{Temperature in Celsius} + 32 \]Given: temperature = \( 27^{\text{C}} \).Formula: \[ \text{Temperature in Fahrenheit} = \frac{9}{5} \times 27 + 32 \]Calculation: \[ \text{Temperature in Fahrenheit} = 48.6 + 32 = 80.6^\text{F} \]Thus, the temperature is 80.6°F.

Key concepts

conversion factors

In chemistry and many other sciences, conversion factors are essential tools. They help us change one unit of measurement to another, allowing for easier calculations and comparisons. Conversion factors are ratios that express how many of one unit equals another. For example, 1 meter equals 3.28084 feet. This means that we multiply any length in meters by 3.28084 to get the length in feet.
Conversion factors can also be used for different types of measurements, such as converting temperatures, volumes, or masses. The key is to know the correct ratio or formula for each conversion.
For instance, to convert Celsius to Fahrenheit, we use the following formula: \[ \text{Temperature in Fahrenheit} = \frac{9}{5} \times \text{Temperature in Celsius} + 32 \] Understanding how to apply conversion factors correctly is vital for solving various scientific problems accurately.

metric to imperial conversion

Converting between metric and imperial units is a common task in science, especially in countries where the metric system is not predominantly used. Let's explore the key conversions needed for the given exercise:
- To convert meters to feet, we use the factor: 1 meter = 3.28084 feet. So, to convert wave heights of 1.5 meters and 4 meters, multiply them by 3.28084 to get 4.92126 feet and 13.12336 feet, respectively.
- Metric to imperial conversions also apply to other measurements, such as volume (liters to gallons) and mass (kilograms to pounds). Each has its specific conversion factor.
Understanding and remembering these conversion factors help streamline calculations when dealing with different measurement systems. This makes cross-system comparisons and practical applications much easier.

temperature conversion

Temperature conversions are crucial, especially when the two primary systems we use are Celsius (metric) and Fahrenheit (imperial). In scientific work, temperature readings may need to be converted to match the standard system for precise communication and analysis.
Using the formula for Celsius to Fahrenheit conversion: \[ \text{Temperature in Fahrenheit} = \frac{9}{5} \times \text{Temperature in Celsius} + 32 \]
We can convert 27°C to Fahrenheit. First, multiply 27 by \(\frac{9}{5}\), which equals 48.6. Then, add 32, resulting in 80.6°F.
This formula helps you easily switch between Celsius and Fahrenheit, ensuring you can communicate temperature readings accurately across different systems.
It's also essential for practical applications like weather forecasting, cooking, and many scientific experiments where precise temperature control and understanding are required.