Monitoring environmental changes

Oct 13, 2025 by miodeya.com 47 views

Understanding the Problem

In this problem, we are given a beach that is eroding at a rate of 4 centimeters per year. A realtor wants to convert this rate to millimeters per day. To solve this problem, we need to perform unit conversions and evaluate an expression to obtain the correct units and numerical value.

Step 1: Convert Centimeters to Millimeters

First, we need to convert centimeters to millimeters. We know that 1 centimeter is equal to 10 millimeters. Therefore, we can write the conversion factor as:

1 \text{ cm} = 10 \text{ mm}

Using this conversion factor, we can convert 4 centimeters to millimeters:

4 \text{ cm} = 4 \times 10 \text{ mm} = 40 \text{ mm}

Step 2: Convert Years to Days

Next, we need to convert years to days. We know that 1 year is equal to 365 days (ignoring leap years for simplicity). Therefore, we can write the conversion factor as:

1 \text{ year} = 365 \text{ days}

Using this conversion factor, we can convert 1 year to days:

1 \text{ year} = 365 \text{ days}

Step 3: Evaluate the Expression

Now that we have converted the units, we can evaluate the expression:

\frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}}

Simplifying the expression, we get:

\frac{4 \times 10 \text{ mm}}{365 \text{ days}} = \frac{40 \text{ mm}}{365 \text{ days}}

Conclusion

Therefore, the expression that results in the correct units and numerical value is:

\frac{40 \text{ mm}}{365 \text{ days}}

This expression represents the erosion rate of the beach in millimeters per day.

Discussion

This problem requires a deep understanding of unit conversions and the ability to evaluate expressions with multiple conversion factors. The key to solving this problem is to break it down into smaller steps and to use conversion factors to convert between units.

Example Use Case

This problem has many real-world applications, such as:

Environmental monitoring: Understanding the erosion rate of a beach is crucial for monitoring environmental changes and predicting the impact of climate change.
Infrastructure planning: Knowing the erosion rate of a beach is essential for planning and designing coastal infrastructure, such as seawalls and jetties.
Tourism and recreation: Understanding the erosion rate of a beach can help tourists and recreational users plan their activities and make informed decisions about beach safety.

Conclusion

In conclusion, converting the erosion rate of a beach from centimeters per year to millimeters per day requires a deep understanding of unit conversions and the ability to evaluate expressions with multiple conversion factors. The expression that results in the correct units and numerical value is:

\frac{40 \text{ mm}}{365 \text{ days}}

Q: What is the erosion rate of the beach in millimeters per day?

A: The erosion rate of the beach is 40 mm per 365 days, which can be simplified to approximately 0.11 mm per day.

Q: How do I convert centimeters to millimeters?

A: To convert centimeters to millimeters, you can multiply the number of centimeters by 10. For example, 4 cm is equal to 4 x 10 mm = 40 mm.

Q: How do I convert years to days?

A: To convert years to days, you can multiply the number of years by 365 (ignoring leap years for simplicity). For example, 1 year is equal to 365 days.

Q: What is the correct expression for converting the erosion rate from centimeters per year to millimeters per day?

A: The correct expression is:

\frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{1 \text{ year}}{365 \text{ days}}

Q: How do I simplify the expression?

A: To simplify the expression, you can cancel out the units and multiply the remaining numbers. For example:

\frac{4 \times 10 \text{ mm}}{365 \text{ days}} = \frac{40 \text{ mm}}{365 \text{ days}}

Q: What are some real-world applications of understanding the erosion rate of a beach?

A: Understanding the erosion rate of a beach has many real-world applications, such as:

Environmental monitoring: Understanding the erosion rate of a beach is crucial for monitoring environmental changes and predicting the impact of climate change.
Infrastructure planning: Knowing the erosion rate of a beach is essential for planning and designing coastal infrastructure, such as seawalls and jetties.
Tourism and recreation: Understanding the erosion rate of a beach can help tourists and recreational users plan their activities and make informed decisions about beach safety.

Q: How can I use this knowledge in my daily life?

A: You can use this knowledge in your daily life by:

Planning beach activities: Understanding the erosion rate of a beach can help you plan your beach activities and make informed decisions about beach safety.
Monitoring environmental changes: Understanding the erosion rate of a beach can help you monitor environmental changes and predict the impact of climate change.
Designing coastal infrastructure: Knowing the erosion rate of a beach is essential for designing coastal infrastructure, such as seawalls and jetties.

Q: What are some common mistakes to avoid when converting units?

A: Some common mistakes to avoid when converting units include:

Not using conversion factors: Failing to use conversion factors can lead to incorrect results.
Not canceling out units: Failing to cancel out units can lead to incorrect results.
Not simplifying expressions: Failing to simplify expressions can lead to incorrect results.

Conclusion

In conclusion, understanding the erosion rate of a beach is crucial for many real-world applications, such as environmental monitoring, infrastructure planning, and tourism and recreation. By using conversion factors and simplifying expressions, you can convert the erosion rate from centimeters per year to millimeters per day. Remember to avoid common mistakes, such as not using conversion factors, not canceling out units, and not simplifying expressions.