Converting Centimeters to Millimeters

Oct 13, 2025 by talynt.org 98 views

Understanding the Problem

A particular beach is experiencing erosion at a rate of 4 centimeters per year. A realtor needs to convert this rate to millimeters per day to better understand the situation. This requires converting the units from centimeters to millimeters and from years to days.

Converting Centimeters to Millimeters

To convert centimeters to millimeters, we need to remember that 1 centimeter is equal to 10 millimeters. This means that 4 centimeters is equal to 4 x 10 = 40 millimeters.

Converting Years to Days

To convert years to days, we need to remember that 1 year is equal to 365 days (ignoring leap years for simplicity). This means that 1 year is equal to 365 days.

Converting Erosion Rate from Centimeters per Year to Millimeters per Day

Now that we have converted the units, we can convert the erosion rate from centimeters per year to millimeters per day. We can do this by multiplying the erosion rate in centimeters per year by the number of millimeters in a centimeter and the number of days in a year.

Expression Evaluation

The expression that we need to evaluate is:

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

Step-by-Step Evaluation

To evaluate this expression, we need to follow the order of operations (PEMDAS):

Multiply the number of millimeters in a centimeter by the number of days in a year:

$\frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{365 \text{ days}}{1 \text{ year}} = \frac{3650 \text{ mm} \times \text{days}}{1 \text{ cm} \times \text{year}}$

Multiply the erosion rate in centimeters per year by the result:

$\frac{4 \text{ cm}}{1 \text{ year}} \times \frac{3650 \text{ mm} \times \text{days}}{1 \text{ cm} \times \text{year}} = \frac{14600 \text{ mm} \times \text{days}}{1 \text{ year}}$

Simplify the expression:

$\frac{14600 \text{ mm} \times \text{days}}{1 \text{ year}} = 14600 \text{ mm} \times \text{days/year}$

Final Expression

The final expression that we need to evaluate is:

$14600 \text{ mm} \times \text{days/year}$

Evaluating the Final Expression

To evaluate this expression, we need to multiply the number of millimeters by the number of days per year:

$14600 \text{ mm} \times \text{days/year} = 14600 \text{ mm/day}$

Conclusion

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

$14600 \text{ mm/day}$

This means that the beach is eroding at a rate of 14600 millimeters per day.

Alternative Expression

An alternative expression that results in the correct units and numerical value is:

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

This expression can be evaluated as follows:

$\frac{4 \text{ cm}}{1 \text{ year}} \times \frac{10 \text{ mm}}{1 \text{ cm}} \times \frac{365 \text{ days}}{1 \text{ year}} = \frac{14600 \text{ mm} \times \text{days}}{1 \text{ year}}$

This expression also results in the correct units and numerical value.

Discussion

The problem requires converting the erosion rate from centimeters per year to millimeters per day. This requires converting the units from centimeters to millimeters and from years to days. The correct expression that results in the correct units and numerical value is:

$14600 \text{ mm/day}$

This means that the beach is eroding at a rate of 14600 millimeters per day.

Conclusion

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

$14600 \text{ mm/day}$

This means that the beach is eroding at a rate of 14600 millimeters per day.

Final Answer

The final answer is: $\boxed{14600}$

Q: What is the erosion rate of the beach in centimeters per year?

A: The erosion rate of the beach is 4 centimeters per year.

Q: Why do we need to convert the erosion rate from centimeters per year to millimeters per day?

A: We need to convert the erosion rate from centimeters per year to millimeters per day to better understand the situation and to make it easier to compare with other rates.

Q: How do we convert centimeters to millimeters?

A: We convert centimeters to millimeters by multiplying the number of centimeters by 10, since 1 centimeter is equal to 10 millimeters.

Q: How do we convert years to days?

A: We convert years to days by multiplying the number of years by 365, since 1 year is equal to 365 days.

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

A: The correct expression to convert the erosion rate from centimeters per year to millimeters per day is:

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

Q: What is the result of evaluating the expression?

A: The result of evaluating the expression is:

$14600 \text{ mm/day}$

Q: What does the result mean?

A: The result means that the beach is eroding at a rate of 14600 millimeters per day.

Q: Is there an alternative expression that can be used to convert the erosion rate from centimeters per year to millimeters per day?

A: Yes, there is an alternative expression that can be used to convert the erosion rate from centimeters per year to millimeters per day:

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

Q: What is the result of evaluating the alternative expression?

A: The result of evaluating the alternative expression is also:

$14600 \text{ mm/day}$

Q: Why is it important to convert the erosion rate from centimeters per year to millimeters per day?

A: It is important to convert the erosion rate from centimeters per year to millimeters per day because it makes it easier to compare with other rates and to understand the situation better.

Q: Can the erosion rate be converted to other units?

A: Yes, the erosion rate can be converted to other units, such as meters per year or kilometers per year.

Q: How do we convert the erosion rate to other units?

A: We convert the erosion rate to other units by multiplying or dividing the number of millimeters by the conversion factor.

Q: What is the conversion factor for millimeters to meters?

A: The conversion factor for millimeters to meters is 1 meter = 1000 millimeters.

Q: What is the conversion factor for millimeters to kilometers?

A: The conversion factor for millimeters to kilometers is 1 kilometer = 1000000 millimeters.

Q: Can the erosion rate be converted to other units using the same expression?

A: Yes, the erosion rate can be converted to other units using the same expression by multiplying or dividing the number of millimeters by the conversion factor.

Q: What is the result of converting the erosion rate from millimeters per day to meters per year?

A: The result of converting the erosion rate from millimeters per day to meters per year is:

$0.0146 \text{ m/year}$

Q: What is the result of converting the erosion rate from millimeters per day to kilometers per year?

A: The result of converting the erosion rate from millimeters per day to kilometers per year is:

$0.0000146 \text{ km/year}$