A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which expression, when evaluated, results in the correct units and numerical value?
$\frac{4 cm}{1 \text { year }} \times \frac{10 mm}{1 cm} \times \frac{1 \text { year }}{365 \text { days }}$
$\frac{4 cm}{1 \text { year }} \times \frac{1 mm}{10 cm} \times \frac{1 \text { year }}{365 \text { days }}$
$\frac{4 cm}{1 \text { year }} \times \frac{1 cm}{10 mm} \times \frac{365 \text { days }}{1 \text { year }}$
$\frac{4 cm}{1 \text { year }} \times \frac{10 mm}{1 cm} \times \frac{365 \text { days }}{1 \text { year }}$
Answer (2)
Convert centimeters to millimeters using the factor 1 cm 10 mm .
Convert years to days using the factor 365 days 1 year .
Multiply the initial rate by the conversion factors: 1 year 4 cm × 1 cm 10 mm × 365 days 1 year .
The correct expression is 1 year 4 c m × 1 c m 10 mm × 365 days 1 year .
Explanation
Understanding the Problem We need to convert the rate of beach erosion from centimeters per year to millimeters per day. We are given four expressions and must choose the one that correctly performs this conversion.
Identifying Conversions The initial rate is 1 year 4 cm . We need to convert centimeters to millimeters and years to days.
Stating Conversion Factors We know that 1 cm = 10 mm, so the conversion factor is 1 cm 10 mm . We also know that 1 year = 365 days, so the conversion factor is 365 days 1 year .
Applying Conversions To convert the rate, we multiply the initial rate by the conversion factors: 1 year 4 cm × 1 cm 10 mm × 365 days 1 year
Identifying the Correct Expression Comparing this expression with the given options, we find that the first option matches exactly.
Final Answer Therefore, the correct expression is: 1 year 4 cm × 1 cm 10 mm × 365 days 1 year
Examples
Understanding unit conversions is crucial in many real-world scenarios. For instance, when planning a road trip, you might need to convert kilometers to miles to match the units on your car's speedometer. Similarly, in cooking, you often convert between grams and ounces. In construction, converting between feet and meters is essential for accurate measurements. These conversions ensure that measurements are consistent and understandable, preventing errors and facilitating clear communication.
The correct mathematical expression to convert the beach erosion rate of 4 cm per year to mm per day is 1 year 4 cm × 1 cm 10 mm × 365 days 1 year . This expression correctly applies the conversion factors for centimeters to millimeters and years to days. Therefore, the first option is the correct choice.
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